Select knots
Up to 7 crossings
8 crossings
9 crossings
10 crossings
11 alternating
11 non-alternating
12 alternating
12 non-alternating
all knots up to 12 crossings maybe slow
discussion of unknown values
statistics of invariants
introduction and help
Download KNOTORIOUS (32 bit version)
Download KNOTORIOUS (64 bit version)
Shorthands denote
u_a algebraic unknotting number
Nak Nakanishi index
det determinant
sign signature
max LT maximum absolute value of
Levine-Tristram signatures
Hidden features
Click on to see
algebraic unknotting number how it has been detected
Alexander polynomial a Seifert matrix
(nondegenerate representative in the S-equivalence class)
Nakanishi index generator of the Alexander module,
if Nakanishi index is 1
Determinant H_1 of the double branched cover


Welcome to the
KNOTORIOUS
world wide web page!
set up by Maciej Borodzik mcboro'at'mimuw;edu;pl
and Stefan Friedl sfriedl'at'gmail;com
last update of the webpage 19 Feb 2012
last update of the knotorious data 01 Dec 2011
You may freely contact the authors in case of any questions.

Knot u_a Alexander
polynomial 		Nak.
index 		det. sign max LT.
12n_0001
1

detected by
an unknotting move
-1+5t-13t^2+19t^3-13t^4+5t^5-t^6
Seifert matrix of 12n_0001
-1 0 0 0 0 -1
0 -2 1 1 1 0
0 0 1 0 0 0
0 1 -1 0 0 0
0 1 -1 -1 0 0
0 0 0 -1 -1 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
57
First homology
of the double branched cover of 12n_0001
Z/57
0 0
12n_0002
1

detected by
an unknotting move
-1+5t-11t^2+16t^3-17t^4+16t^5-11t^6+5t^7-t^8
Seifert matrix of 12n_0002
-1 0 -1 -1 -1 -1 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 -1 -1 0 0
0 1 -1 0 -1 0 0 0
0 1 -1 0 -1 -1 0 0
0 0 0 0 -1 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(-t,0,1,0,1,1,-1,0)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-4+4t-3t^2+t^3
83
First homology
of the double branched cover of 12n_0002
Z/83
-2 2
12n_0003
1

detected by
an unknotting move
-1+7t-17t^2+23t^3-17t^4+7t^5-t^6
Seifert matrix of 12n_0003
-1 0 0 0 0 -1
0 0 1 1 1 0
0 0 1 0 0 0
0 1 -1 0 0 0
0 1 -1 -1 0 0
0 0 0 -1 -1 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+6t^-1-9+6t-t^2
73
First homology
of the double branched cover of 12n_0003
Z/73
0 0
12n_0004
1

detected by
an unknotting move
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 12n_0004
-1 0 -1 0 0 1
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 -1 -1 -1
0 0 0 0 0 -1
0 -1 1 0 -1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
1
81
First homology
of the double branched cover of 12n_0004
Z/81
0 0
12n_0005
1

detected by
an unknotting move
1-7t+21t^2-29t^3+21t^4-7t^5+t^6
Seifert matrix of 12n_0005
-1 0 -1 -1 1 -1
0 1 0 0 0 0
0 0 1 0 0 0
0 1 -1 0 2 -1
0 -1 1 1 1 0
0 1 -1 0 1 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+5t^-1-10+5t-t^2
87
First homology
of the double branched cover of 12n_0005
Z/87
2 2
12n_0006
2

detected by
the signature
1-5t+9t^2-6t^3+3t^4-6t^5+9t^6-5t^7+t^8
Seifert matrix of 12n_0006
-1 0 -1 -1 -1 -1 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 -1 -1 0 0
0 1 -1 0 -1 0 0 0
0 1 -1 0 -1 -1 0 0
0 0 0 0 -1 -1 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,-t,t^2)
the Blanchfield form on it
t^-3-4t^-2+5t^-1-2+5t-4t^2+t^3
45
First homology
of the double branched cover of 12n_0006
Z/45
-4 4
12n_0007
1

detected by
an unknotting move
1-5t+9t^2-9t^3+9t^4-5t^5+t^6
Seifert matrix of 12n_0007
1 0 0 0 0 0
-1 0 1 -1 0 -1
1 1 -2 0 1 1
0 0 0 -1 0 0
-1 -1 1 -1 0 -1
-1 0 1 -1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+6t^-1-11+6t-t^2
39
First homology
of the double branched cover of 12n_0007
Z/39
2 2
12n_0008
2

detected by
the signature
1-5t+9t^2-10t^3+11t^4-10t^5+9t^6-5t^7+t^8
Seifert matrix of 12n_0008
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 -1 -1 -1
0 0 -1 0 0 0 0 0
-1 0 -1 -1 0 -1 -1 -1
0 0 0 0 1 0 0 0
-1 0 -1 0 -1 -1 -1 -1
-1 0 -1 0 -1 0 -1 0
-1 0 -1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
t^-3-5t^-2+8t^-1-7+8t-5t^2+t^3
61
First homology
of the double branched cover of 12n_0008
Z/61
-4 4
12n_0009
1

detected by
an unknotting move
1-7t+17t^2-21t^3+17t^4-7t^5+t^6
Seifert matrix of 12n_0009
1 0 0 0 0 0
-1 0 1 -1 0 -1
1 1 0 0 1 1
0 0 0 -1 0 0
-1 -1 1 -1 0 -1
-1 0 1 -1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+6t^-1-11+6t-t^2
71
First homology
of the double branched cover of 12n_0009
Z/71
2 2
12n_0010
2

detected by
the Lickorish test
1-5t+9t^2-9t^3+9t^4-5t^5+t^6
Seifert matrix of 12n_0010
1 0 0 0 0 0
-1 -1 0 -1 1 -1
0 0 1 0 0 0
-1 0 -1 0 1 -1
1 0 1 1 -2 1
-1 0 -1 0 1 0
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+10t^-1-17+10t-2t^2
39
First homology
of the double branched cover of 12n_0010
Z/39
2 2
12n_0011
1

detected by
an unknotting move
3-15t+25t^2-15t^3+3t^4
Seifert matrix of 12n_0011
1 0 0 0
1 1 -1 1
1 -1 -2 0
0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
61
First homology
of the double branched cover of 12n_0011
Z/61
0 0
12n_0012
1

detected by
an unknotting move
2-10t+18t^2-19t^3+18t^4-10t^5+2t^6
Seifert matrix of 12n_0012
1 0 0 0 0 0
-1 -1 0 -1 0 1
0 0 -1 0 0 0
-1 0 -1 -1 0 1
0 0 0 0 1 0
1 0 1 0 1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
79
First homology
of the double branched cover of 12n_0012
Z/79
-2 2
12n_0013
1

detected by
an unknotting move
1-7t+13t^2-7t^3+t^4
Seifert matrix of 12n_0013
1 0 0 0
1 1 -1 1
1 -1 0 0
0 0 0 -1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-t^-1+2-t
29
First homology
of the double branched cover of 12n_0013
Z/29
0 0
12n_0014
1

detected by
an unknotting move
-1+7t-21t^2+31t^3-21t^4+7t^5-t^6
Seifert matrix of 12n_0014
-2 -2 1 -3 0 -1
-1 -1 1 -2 0 -1
0 0 1 0 0 0
-2 -3 1 -4 0 -2
-1 0 0 -1 -1 -1
-1 -1 0 -2 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-2-6t^-1+11-6t+t^2
89
First homology
of the double branched cover of 12n_0014
Z/89
0 0
12n_0015
2

detected by
the Lickorish test
1-9t+27t^2-37t^3+27t^4-9t^5+t^6
Seifert matrix of 12n_0015
1 1 0 -1 0 1
0 -2 2 1 0 -1
0 0 1 0 0 0
0 1 -1 0 0 0
-1 0 0 0 -1 0
0 -2 1 1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+6t^-1-9+6t-t^2
111
First homology
of the double branched cover of 12n_0015
Z/111
2 2
12n_0016
2

detected by
the signature
1-5t+7t^2-5t^4+7t^6-5t^7+t^8
Seifert matrix of 12n_0016
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 -1 0 0 -1
0 0 0 0 0 1 0 -1
0 0 0 0 -1 0 -1 -1
0 -1 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,t,0,1)
the Blanchfield form on it
t^-3-3t^-2+2t^-1-1+2t-3t^2+t^3
21
First homology
of the double branched cover of 12n_0016
Z/21
-4 4
12n_0017
2

detected by
the Lickorish test
1-8t+22t^2-29t^3+22t^4-8t^5+t^6
Seifert matrix of 12n_0017
1 0 0 0 0 0
-1 -1 0 1 0 1
0 0 1 0 0 0
1 0 1 1 0 0
0 0 0 0 -1 -1
1 0 1 0 0 1
1
Generator of the Alexander module
(0,0,2-t,2-t,3+t-t^2,0)
the Blanchfield form on it
-2t^-2+11t^-1-15+11t-2t^2
91
First homology
of the double branched cover of 12n_0017
Z/91
2 2
12n_0018
1

detected by
an unknotting move
-1+8t-26t^2+39t^3-26t^4+8t^5-t^6
Seifert matrix of 12n_0018
1 0 0 0 0 0
-1 -1 0 1 0 1
0 0 1 0 0 0
1 0 1 -1 0 0
0 0 0 0 1 -1
1 0 1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+5t^-1-9+5t-t^2
109
First homology
of the double branched cover of 12n_0018
Z/109
0 0
12n_0019
1

detected by
an unknotting move
1-3t-t^2+7t^3-t^4-3t^5+t^6
Seifert matrix of 12n_0019
1 0 0 0 0 0
-1 -1 0 1 0 1
0 0 -1 -1 0 -1
1 0 0 0 0 -1
0 0 0 0 -1 -1
1 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,-t,1,1+t,0)
the Blanchfield form on it
-2t^-2+t^-1+7+t-2t^2
1
First homology
of the double branched cover of 12n_0019
0
0 0
12n_0020
1

detected by
an unknotting move
1-5t+11t^2-13t^3+11t^4-5t^5+t^6
Seifert matrix of 12n_0020
1 0 0 0 0 0
0 0 0 -1 0 -1
0 0 1 0 0 0
0 -1 1 -2 0 -2
0 -1 0 -1 -1 -1
-1 0 1 -1 0 0
1
Generator of the Alexander module
(0,0,0,1,1,0)
the Blanchfield form on it
t^-1-2+t
47
First homology
of the double branched cover of 12n_0020
Z/47
2 2
12n_0021
1

detected by
an unknotting move
2-12t+28t^2-35t^3+28t^4-12t^5+2t^6
Seifert matrix of 12n_0021
1 0 0 0 0 0
-1 -2 -1 0 0 -1
0 -1 -2 0 0 0
0 -1 -1 -1 0 0
0 -1 -1 0 -1 0
-1 0 1 1 0 0
1
Generator of the Alexander module
(0,8t-3t^2,0,1-5t+3t^2,9t-8t^2+3t^3,0)
the Blanchfield form on it
-2t^-1+4-2t
119
First homology
of the double branched cover of 12n_0021
Z/119
-2 2
12n_0022
1

detected by
an unknotting move
1-6t+16t^2-29t^3+37t^4-29t^5+16t^6-6t^7+t^8
Seifert matrix of 12n_0022
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 0
0 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 -1 -1
0 0 0 0 1 1 0 1
0 0 0 0 0 1 0 0
-1 0 -1 0 -1 0 -1 0
0 0 0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,0,-1-3t^2+t^3-2t^4+t^5,2+3t^2-t^3+2t^4-t^5,0,-1-t-3t^2-t^3-t^4+t^5,0)
the Blanchfield form on it
x
141
First homology
of the double branched cover of 12n_0022
Z/141
0 0
12n_0023
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 12n_0023
-4 -2
-1 0
1
Generator of the Alexander module
(1-2t,1)
the Blanchfield form on it
-2
9
First homology
of the double branched cover of 12n_0023
Z/9
0 0
12n_0024
1

detected by
an unknotting move
-1+5t-11t^2+15t^3-11t^4+5t^5-t^6
Seifert matrix of 12n_0024
-1 1 0 1 0 1
0 0 0 -1 0 -1
0 0 1 0 0 0
0 -1 -1 -2 0 -2
-1 1 0 1 -1 1
0 0 -1 -1 0 0
1
Generator of the Alexander module
(0,1,0,0,1+t,2)
the Blanchfield form on it
t^-1-2+t
49
First homology
of the double branched cover of 12n_0024
Z/49
0 0
12n_0025
1

detected by
an unknotting move
-1+3t-3t^2+3t^3-t^4
Seifert matrix of 12n_0025
3 1 -1 5
2 1 -1 3
0 0 1 0
6 2 -1 9
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-1-1+t
11
First homology
of the double branched cover of 12n_0025
Z/11
2 2
12n_0026
1

detected by
an unknotting move
-2+10t-22t^2+29t^3-22t^4+10t^5-2t^6
Seifert matrix of 12n_0026
-1 0 0 0 -1 -1
0 -2 1 0 0 -1
0 0 1 0 0 0
0 0 0 0 0 -1
0 0 0 -1 0 -1
0 -1 1 -1 -1 -2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-2t^-1+5-2t
97
First homology
of the double branched cover of 12n_0026
Z/97
0 0
12n_0027
2

detected by
the Lickorish test
-1+6t-16t^2+25t^3-27t^4+25t^5-16t^6+6t^7-t^8
Seifert matrix of 12n_0027
-1 0 -1 -1 -1 0 -1 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 0 0
0 1 -1 -1 -1 0 0 0
0 0 0 -1 -1 1 -1 1
0 1 -1 -1 -1 0 -1 0
0 0 0 0 -1 0 -1 1
1
Generator of the Alexander module
(0,0,0,t,0,1,0,-t)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
123
First homology
of the double branched cover of 12n_0027
Z/123
-2 2
12n_0028
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 12n_0028
-2 1 0 -2
1 0 0 1
-2 1 0 -3
-3 1 -2 -4
1
Generator of the Alexander module
(0,0,1,-1+t)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
33
First homology
of the double branched cover of 12n_0028
Z/33
0 0
12n_0029
1

detected by
an unknotting move
2-12t+28t^2-35t^3+28t^4-12t^5+2t^6
Seifert matrix of 12n_0029
-1 0 0 -1 0 -1
0 -2 1 0 0 -1
0 0 1 0 0 0
0 0 0 0 0 -1
-1 0 0 0 -1 -1
0 -1 1 -1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-1+5-2t
119
First homology
of the double branched cover of 12n_0029
Z/119
-2 2
12n_0030
1

detected by
an unknotting move
1-6t+16t^2-29t^3+37t^4-29t^5+16t^6-6t^7+t^8
Seifert matrix of 12n_0030
-1 0 -1 -1 0 0 -1 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 0 0
0 0 0 0 1 0 -1 0
0 0 0 -1 1 1 -1 1
0 1 -1 -1 0 0 -1 0
0 0 0 -1 1 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,-1,-1,0,0)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
141
First homology
of the double branched cover of 12n_0030
Z/141
0 0
12n_0031
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 12n_0031
-7 -5
-6 -4
1
Generator of the Alexander module
(2-t-2t^2,1-t-2t^2)
the Blanchfield form on it
-2
9
First homology
of the double branched cover of 12n_0031
Z/9
0 0
12n_0032
1

detected by
an unknotting move
-2+10t-22t^2+29t^3-22t^4+10t^5-2t^6
Seifert matrix of 12n_0032
1 0 0 0 0 0
-1 0 1 1 0 -1
1 1 -2 -1 -1 1
1 1 -1 -2 -1 1
1 1 -1 -2 -2 1
-1 0 1 1 0 0
1
Generator of the Alexander module
(0,t,1,0,0,0)
the Blanchfield form on it
2t^-2-8t^-1+12-8t+2t^2
97
First homology
of the double branched cover of 12n_0032
Z/97
0 0
12n_0033
2

detected by
the Lickorish test
-1+6t-16t^2+25t^3-27t^4+25t^5-16t^6+6t^7-t^8
Seifert matrix of 12n_0033
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 -1
0 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1
0 0 0 0 1 1 0 0
0 0 0 0 0 1 0 0
-1 0 -1 0 -1 0 -1 0
-1 0 -1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,1,-1,t,0,0,-1,t)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
123
First homology
of the double branched cover of 12n_0033
Z/123
-2 2
12n_0034
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 12n_0034
2 0 1 0
0 0 1 0
0 1 0 -1
0 1 -1 -2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
33
First homology
of the double branched cover of 12n_0034
Z/33
0 0
12n_0035
1

detected by
an unknotting move
-1+6t-16t^2+23t^3-16t^4+6t^5-t^6
Seifert matrix of 12n_0035
-1 0 0 0 0 -1
0 0 0 0 -1 0
0 0 1 0 0 0
-1 0 0 1 0 0
0 -1 1 0 -2 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+4t^-1-7+4t-t^2
69
First homology
of the double branched cover of 12n_0035
Z/69
0 0
12n_0036
1

detected by
an unknotting move
1-8t+22t^2-29t^3+22t^4-8t^5+t^6
Seifert matrix of 12n_0036
0 2 -1 0 -1 0
1 1 1 0 0 0
0 0 1 0 0 0
0 0 0 -1 0 -1
0 1 -1 0 0 0
1 1 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+6t^-1-9+6t-t^2
91
First homology
of the double branched cover of 12n_0036
Z/91
2 2
12n_0037
2

detected by
the signature
1-5t+8t^2-5t^3+3t^4-5t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0037
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 -1 0
0 -1 -1 0 -1 0 0 0
0 -1 0 0 -1 -1 0 0
0 0 0 0 0 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+2t^-1-1+2t-3t^2+t^3
41
First homology
of the double branched cover of 12n_0037
Z/41
-4 4
12n_0038
1

detected by
an unknotting move
1-6t+16t^2-21t^3+16t^4-6t^5+t^6
Seifert matrix of 12n_0038
0 0 -1 0 1 0
1 1 -1 0 2 0
0 0 1 0 0 0
1 1 0 1 2 0
2 1 -1 0 4 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+4t^-1-7+4t-t^2
67
First homology
of the double branched cover of 12n_0038
Z/67
2 2
12n_0039
1

detected by
an unknotting move
-1+8t-22t^2+31t^3-22t^4+8t^5-t^6
Seifert matrix of 12n_0039
0 2 -1 -1 -1 -1
1 1 1 -1 0 -1
0 0 1 0 0 0
0 0 0 -1 0 -1
0 1 -1 0 0 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1-t,1+t-t^2,0)
the Blanchfield form on it
-t^-2+7t^-1-13+7t-t^2
93
First homology
of the double branched cover of 12n_0039
Z/93
0 0
12n_0040
2

detected by
the Lickorish test
-1+5t-10t^2+11t^3-9t^4+11t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0040
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 -1 0 -1 0 0 0
0 -1 0 0 -1 -1 0 0
0 0 0 1 0 0 1 0
0 0 0 1 0 -1 1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,2-t)
the Blanchfield form on it
t^-3-3t^-2+2t^-1-1+2t-3t^2+t^3
63
First homology
of the double branched cover of 12n_0040
Z/63
-2 2
12n_0041
1

detected by
an unknotting move
1-4t+4t^2-t^3+4t^4-4t^5+t^6
Seifert matrix of 12n_0041
1 0 0 0 0 0
-1 0 1 0 -1 0
1 1 -2 1 0 1
-1 -1 1 0 0 0
0 0 0 0 -1 0
-1 -1 1 -1 0 0
1
Generator of the Alexander module
(0,-1-t,t,0,0,1+t^2)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
19
First homology
of the double branched cover of 12n_0041
Z/19
2 2
12n_0042
1

detected by
an unknotting move
1-6t+14t^2-17t^3+14t^4-6t^5+t^6
Seifert matrix of 12n_0042
1 0 0 0 0 0
0 -1 0 0 -1 0
1 0 -2 0 0 1
0 -1 0 -1 -1 0
0 0 0 0 -1 0
-1 -1 1 -1 -1 0
1
Generator of the Alexander module
(0,0,-1,1,0,2)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
59
First homology
of the double branched cover of 12n_0042
Z/59
-2 2
12n_0043
1

detected by
an unknotting move
1-5t+10t^2-15t^3+19t^4-15t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0043
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 0
0 0 -1 0 0 0 0 0
-1 0 -1 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 1
-1 0 -1 0 -1 -1 -1 -1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
81
First homology
of the double branched cover of 12n_0043
Z/81
0 0
12n_0044
1

detected by
an unknotting move
1-6t+12t^2-13t^3+12t^4-6t^5+t^6
Seifert matrix of 12n_0044
1 0 0 0 0 0
0 -1 0 0 -1 0
1 0 0 0 0 1
0 -1 0 -1 -1 0
0 0 0 0 -1 0
-1 -1 1 -1 -1 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+2t^-1-2+2t-t^2
51
First homology
of the double branched cover of 12n_0044
Z/51
-2 2
12n_0045
1

detected by
an unknotting move
-1+4t-8t^2+11t^3-8t^4+4t^5-t^6
Seifert matrix of 12n_0045
0 1 -1 0 -1 0
1 -2 1 0 1 0
0 0 1 0 0 0
-1 0 0 -1 0 -1
0 1 -1 0 0 0
-1 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
37
First homology
of the double branched cover of 12n_0045
Z/37
0 0
12n_0046
1

detected by
an unknotting move
2-10t+17t^2-10t^3+2t^4
Seifert matrix of 12n_0046
1 0 0 0
0 -2 0 0
1 0 -2 1
-1 1 1 0
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-1+2-t
41
First homology
of the double branched cover of 12n_0046
Z/41
0 0
12n_0047
1

detected by
an unknotting move
2-9t+13t^2-11t^3+13t^4-9t^5+2t^6
Seifert matrix of 12n_0047
1 0 0 0 0 0
-1 -1 0 -1 -1 0
0 0 -1 0 0 0
-1 0 -1 -1 -1 0
-1 0 -1 0 -1 1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,0,1,1,0,0)
the Blanchfield form on it
-t^-2+2t^-1+2t-t^2
59
First homology
of the double branched cover of 12n_0047
Z/59
-2 2
12n_0048
1

detected by
an unknotting move
2-12t+21t^2-12t^3+2t^4
Seifert matrix of 12n_0048
1 0 0 0
0 -2 0 0
1 0 0 1
-1 1 1 0
1
Generator of the Alexander module
(0,1,-t,-t)
the Blanchfield form on it
t^-1-4+t
49
First homology
of the double branched cover of 12n_0048
Z/49
0 0
12n_0049
1

detected by
an unknotting move
4-20t+33t^2-20t^3+4t^4
Seifert matrix of 12n_0049
1 0 0 0
-1 -5 -4 -7
0 -4 -5 -6
-1 -6 -5 -8
1
Generator of the Alexander module
(0,4-2t+6t^2-4t^3,1+6t^2-4t^3,1+6t^2-4t^3)
the Blanchfield form on it
106t^-2-551t^-1+926-551t+106t^2
81
First homology
of the double branched cover of 12n_0049
Z/81
0 0
12n_0050
1

detected by
an unknotting move
2-11t+23t^2-27t^3+23t^4-11t^5+2t^6
Seifert matrix of 12n_0050
1 0 0 0 0 0
-1 -1 0 0 1 -1
0 0 -1 0 0 0
0 0 0 1 0 0
1 0 1 0 -2 1
-1 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,-1-t-34t^2+12t^3+64t^4-38t^5+44t^6+28t^7-56t^8+16t^9,1+2t+36t^2+26t^3-38t^4+72t^5-64t^6+16t^7,1+t+36t^2-10t^3+8t^4+18t^5-28t^6+8t^7,t+2t^2+37t^3+26t^4-2t^5+26t^6-10t^7-20t^8+8t^9,3+35t^2-46t^3+18t^4+10t^5-46t^6+36t^7-8t^8)
the Blanchfield form on it
x
99
First homology
of the double branched cover of 12n_0050
Z/99
-2 2
12n_0051
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 12n_0051
-11 2
1 0
1
Generator of the Alexander module
(-5+3t+2t^2,1)
the Blanchfield form on it
-1
9
First homology
of the double branched cover of 12n_0051
Z/9
0 0
12n_0052
2

detected by
the Lickorish test
1-9t+30t^2-43t^3+30t^4-9t^5+t^6
Seifert matrix of 12n_0052
1 0 0 0 0 0
-1 -1 0 0 1 -1
0 0 1 0 0 0
0 0 0 1 0 0
1 0 1 0 1 1
-1 0 -1 -1 0 -1
1 or 2
123
First homology
of the double branched cover of 12n_0052
Z/123
2 2
12n_0053
1

detected by
an unknotting move
3-14t+23t^2-14t^3+3t^4
Seifert matrix of 12n_0053
1 0 0 0
1 -2 -1 -3
1 -1 0 -2
2 -2 -2 -5
1
Generator of the Alexander module
(0,1,1,0)
the Blanchfield form on it
t^-1-2+t
57
First homology
of the double branched cover of 12n_0053
Z/57
0 0
12n_0054
2

detected by
the signature
-1+4t-6t^2+7t^3-6t^4+4t^5-t^6
Seifert matrix of 12n_0054
1 0 0 0 0 0
0 0 0 0 -1 -1
0 0 1 0 0 0
1 0 0 1 0 0
0 -1 -1 0 -2 -2
-1 0 -1 -1 -1 0
1
Generator of the Alexander module
(0,0,0,t^2,1+t-t^3,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
29
First homology
of the double branched cover of 12n_0054
Z/29
4 4
12n_0055
2

detected by
the Lickorish test
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 12n_0055
-1 -1 0 -1 0 0
0 -2 1 -4 0 -2
0 0 1 0 0 0
0 -4 2 -6 0 -3
0 -1 0 -1 -1 0
0 -1 1 -2 1 -2
2
111
First homology
of the double branched cover of 12n_0055
Z/111
-2 2
12n_0056
2

detected by
A(F_2)
1-2t+3t^2-2t^3+t^4
Seifert matrix of 12n_0056
-1 1 1 0
0 0 -1 0
0 0 2 -1
-1 0 -1 0
2
9
First homology
of the double branched cover of 12n_0056
Z/9
0 0
12n_0057
2

detected by
A(F_2)
1-2t+3t^2-2t^3+t^4
Seifert matrix of 12n_0057
0 -1 1 0
0 0 1 0
0 1 0 1
1 -1 1 1
2
9
First homology
of the double branched cover of 12n_0057
Z/9
0 0
12n_0058
2

detected by
the signature
-2+13t-30t^2+39t^3-30t^4+13t^5-2t^6
Seifert matrix of 12n_0058
0 3 -1 2 1 1
2 4 1 2 2 2
0 0 1 0 0 0
1 1 1 1 1 1
1 3 0 2 2 2
1 2 0 1 1 2
2
129
First homology
of the double branched cover of 12n_0058
Z/129
4 4
12n_0059
2

detected by
the signature
-1+3t-8t^3+13t^4-8t^5+3t^7-t^8
Seifert matrix of 12n_0059
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 -1 -1 0 0
0 -1 0 -1 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
21
First homology
of the double branched cover of 12n_0059
Z/21
-4 4
12n_0060
2

detected by
the Lickorish test
-1+5t-12t^2+20t^3-23t^4+20t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0060
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 1 1 0 0
0 0 0 0 0 1 0 0
0 -1 0 -1 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
99
First homology
of the double branched cover of 12n_0060
Z/99
-2 2
12n_0061
2

detected by
the Lickorish test
-1+5t-12t^2+20t^3-23t^4+20t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0061
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 -1 -1 0 0
0 -1 0 -1 0 0 1 1
0 0 0 0 0 0 0 1
2
99
First homology
of the double branched cover of 12n_0061
Z/99
-2 2
12n_0062
2

detected by
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0062
-1 0 0 -1 -1 -1
0 -2 1 -1 0 0
0 0 1 0 0 0
0 -1 1 -2 -1 -1
0 0 0 -1 0 0
0 0 0 -1 -1 0
2
81
First homology
of the double branched cover of 12n_0062
Z/81
0 0
12n_0063
2

detected by
the Lickorish test
-3+10t-13t^2+10t^3-3t^4
Seifert matrix of 12n_0063
0 1 0 0
1 0 -1 0
-1 0 7 3
0 1 3 2
2
39
First homology
of the double branched cover of 12n_0063
Z/39
2 2
12n_0064
2

detected by
the signature
1-5t+10t^2-12t^3+13t^4-12t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0064
-1 0 -1 -1 -1 -1 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 -1 -1 0 0
0 1 -1 0 -1 0 0 0
0 1 -1 0 -1 -1 0 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 0 0 -1 -1
2
69
First homology
of the double branched cover of 12n_0064
Z/69
-4 4
12n_0065
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 12n_0065
-2 -1 -1 -2
-1 0 0 -1
0 0 1 0
-1 0 -1 1
1
Generator of the Alexander module
(-t,0,0,1)
the Blanchfield form on it
t^-1-2+t
31
First homology
of the double branched cover of 12n_0065
Z/31
2 2
12n_0066
2

detected by
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0066
1 0 0 0 0 0
-1 0 1 -1 1 1
1 1 -2 1 -1 -1
-1 0 1 0 1 1
1 1 -1 1 -2 -1
1 1 -1 1 -2 -2
2
81
First homology
of the double branched cover of 12n_0066
Z/81
0 0
12n_0067
3

detected by
the signature
1-5t+8t^2-8t^3+7t^4-8t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0067
1 0 0 0 0 0 0 0
-1 -1 0 0 1 1 1 0
0 0 1 0 0 0 0 0
0 0 0 1 1 1 1 0
1 0 1 0 1 1 0 0
1 0 1 0 0 1 0 0
1 0 1 0 1 1 1 0
0 0 0 1 1 1 1 1
2
51
First homology
of the double branched cover of 12n_0067
Z/51
6 6
12n_0068
3

detected by
the signature
1-5t+7t^2-4t^3+t^4-4t^5+7t^6-5t^7+t^8
Seifert matrix of 12n_0068
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
-1 -1 0 -1 0 0 1 0
0 0 -1 -1 -1 -1 0 0
-1 -1 0 -1 0 -1 1 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 -1
1
Generator of the Alexander module
(0,-2+t+2t^2+4t^3,0,1-t^2-2t^3,0,-2t^2+t^3+2t^4+4t^5,0,t^2-t^4-2t^5)
the Blanchfield form on it
x
35
First homology
of the double branched cover of 12n_0068
Z/35
-6 6
12n_0069
1

detected by
an unknotting move
-1+7t-17t^2+23t^3-17t^4+7t^5-t^6
Seifert matrix of 12n_0069
1 0 0 0 0 1
0 -1 0 0 0 0
0 -1 -2 1 1 0
0 0 1 0 0 1
0 0 1 -1 0 1
0 0 0 0 0 -1
1
Generator of the Alexander module
(2t,0,1-t^2,0,t,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
73
First homology
of the double branched cover of 12n_0069
Z/73
0 0
12n_0070
1

detected by
an unknotting move
1-7t+19t^2-25t^3+19t^4-7t^5+t^6
Seifert matrix of 12n_0070
-1 0 0 0 0 1
0 -1 0 0 0 0
0 -1 -2 -1 -2 -2
0 -1 -1 0 -1 -1
0 -1 -1 -1 -2 -1
0 -1 -1 -1 -1 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
79
First homology
of the double branched cover of 12n_0070
Z/79
-2 2
12n_0071
1

detected by
an unknotting move
1-5t+9t^2-10t^3+9t^4-10t^5+9t^6-5t^7+t^8
Seifert matrix of 12n_0071
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 -1 0 0
0 0 -1 0 -1 -1 0 0
-1 -1 0 0 0 -1 1 0
0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+3t^-1-3+3t-2t^2+t^3
59
First homology
of the double branched cover of 12n_0071
Z/59
-2 2
12n_0072
2

detected by
the signature
-1+9t-23t^2+31t^3-23t^4+9t^5-t^6
Seifert matrix of 12n_0072
-1 0 0 0 0 -1
0 -1 0 0 0 0
0 -1 -2 0 1 0
0 0 0 -1 -1 0
0 0 1 0 0 1
0 0 0 0 0 -1
1
Generator of the Alexander module
(1,0,-1,1,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
97
First homology
of the double branched cover of 12n_0072
Z/97
-4 4
12n_0073
2

detected by
the Lickorish test
1-5t+13t^2-17t^3+13t^4-5t^5+t^6
Seifert matrix of 12n_0073
1 0 0 0 0 0
0 -1 0 0 0 0
0 -1 -2 -2 -1 -2
0 -1 -1 0 -1 -1
0 -1 -1 -1 0 -1
1 -1 -1 -1 -1 0
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-1+1-t
55
First homology
of the double branched cover of 12n_0073
Z/55
2 2
12n_0074
4

detected by
the signature
-2+5t-7t^2+7t^3-7t^4+7t^5-7t^6+5t^7-2t^8
Seifert matrix of 12n_0074
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 1 0
0 0 0 -1 0 0 -1 0
0 0 -1 0 -1 0 1 0
0 0 0 0 0 -1 -1 0
1 1 0 0 0 0 -2 0
0 0 0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,t,0,1,0,-t)
the Blanchfield form on it
-2t^-3+3t^-2-3t^-1+2-3t+3t^2-2t^3
49
First homology
of the double branched cover of 12n_0074
Z/49
-8 8
12n_0075
1

detected by
an unknotting move
3-10t+18t^2-21t^3+18t^4-10t^5+3t^6
Seifert matrix of 12n_0075
1 0 0 0 0 0
0 -1 0 0 0 0
0 -1 -2 0 0 -1
0 0 0 1 0 0
1 0 0 0 1 0
1 0 -1 1 1 1
1
Generator of the Alexander module
(0,0,1-t,0,-t,0)
the Blanchfield form on it
-2t^-2+5t^-1-7+5t-2t^2
83
First homology
of the double branched cover of 12n_0075
Z/83
2 2
12n_0076
2

detected by
the signature
-1+6t-12t^2+15t^3-12t^4+6t^5-t^6
Seifert matrix of 12n_0076
-3 -2 0 0 -2 0
-3 -3 0 0 -2 0
0 0 -1 0 0 -1
-1 -1 0 -1 -1 0
-2 -2 0 0 -1 0
-1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,-t,1,0,0)
the Blanchfield form on it
-t^-2+5t^-1-6+5t-t^2
53
First homology
of the double branched cover of 12n_0076
Z/53
-4 4
12n_0077
3

detected by
the signature
3-7t+8t^2-7t^3+8t^4-7t^5+3t^6
Seifert matrix of 12n_0077
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 0 0 -1
0 0 0 -1 0 1
0 0 -1 0 -1 -1
-1 -1 0 0 0 -3
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
43
First homology
of the double branched cover of 12n_0077
Z/43
-6 6
12n_0078
2

detected by
the Lickorish test
5-16t+23t^2-16t^3+5t^4
Seifert matrix of 12n_0078
2 0 1 -1
0 -1 0 0
1 -1 -2 0
0 0 0 1
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
2t^-2-7t^-1+10-7t+2t^2
65
First homology
of the double branched cover of 12n_0078
Z/65
0 0
12n_0079
1

detected by
an unknotting move
-1+6t-9t^2+6t^3-t^4
Seifert matrix of 12n_0079
-4 -3 -3 0
-4 -4 -3 0
-3 -3 -2 0
-1 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
1
23
First homology
of the double branched cover of 12n_0079
Z/23
-2 2
12n_0080
1

detected by
an unknotting move
2-7t+15t^2-19t^3+15t^4-7t^5+2t^6
Seifert matrix of 12n_0080
-1 -1 -1 0 -1 0
0 0 -1 0 -1 -1
0 -1 0 0 -1 0
0 0 0 1 0 0
0 0 -1 0 0 -1
0 0 0 1 0 2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
4t^-2-11t^-1+15-11t+4t^2
67
First homology
of the double branched cover of 12n_0080
Z/67
2 2
12n_0081
2

detected by
the signature
-2+11t-23t^2+29t^3-23t^4+11t^5-2t^6
Seifert matrix of 12n_0081
-1 -1 -1 0 -1 0
0 -2 -1 0 -2 0
0 -1 0 0 -1 0
0 0 0 -1 0 -1
0 -1 -1 0 -2 0
0 1 0 0 1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
101
First homology
of the double branched cover of 12n_0081
Z/101
-4 4
12n_0082
1

detected by
an unknotting move
2-5t+7t^2-7t^3+7t^4-5t^5+2t^6
Seifert matrix of 12n_0082
-1 -1 -1 0 -1 0
0 0 -1 0 -1 -1
0 -1 -2 0 -1 0
0 0 0 1 0 0
0 0 -1 0 0 -1
0 0 0 1 0 2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
3t^-1-5+3t
35
First homology
of the double branched cover of 12n_0082
Z/35
2 2
12n_0083
2

detected by
the signature
-2+11t-24t^2+31t^3-24t^4+11t^5-2t^6
Seifert matrix of 12n_0083
-1 -1 -1 0 -1 0
0 -1 -1 0 -2 0
0 -1 -2 0 -1 0
0 0 0 -1 0 -1
0 -1 -1 0 -1 0
0 1 0 0 1 -2
1
Generator of the Alexander module
(2,0,0,-t+2t^2,0,1-2t)
the Blanchfield form on it
-6t^-2+25t^-1-32+25t-6t^2
105
First homology
of the double branched cover of 12n_0083
Z/105
-4 4
12n_0084
1

detected by
an unknotting move
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 12n_0084
-1 -1 -1 0 -1 0
0 -1 -1 0 -1 -1
0 -1 -2 0 -1 0
0 0 0 1 0 0
0 0 -1 0 -1 -1
0 0 0 1 0 2
1
Generator of the Alexander module
(-3+2t,0,0,0,-2+t,0)
the Blanchfield form on it
4t^-2-8t^-1+13-8t+4t^2
63
First homology
of the double branched cover of 12n_0084
Z/63
-2 2
12n_0085
2

detected by
the Lickorish test
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 12n_0085
-1 -1 0 -1 -1 -1
0 0 0 -1 -1 -1
0 0 -1 -1 -1 -1
0 -1 0 0 -1 -1
0 -1 0 -1 0 -1
0 -1 0 0 -1 0
1
Generator of the Alexander module
(1,0,-2+t,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
65
First homology
of the double branched cover of 12n_0085
Z/65
0 2
12n_0086
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 12n_0086
-1 -1 0 -1 -1 -1
0 0 0 -1 -1 -1
0 0 1 -1 -1 -1
0 -1 0 -2 -1 -2
0 -1 0 -1 -2 -1
0 -1 0 -1 -1 -2
1
Generator of the Alexander module
(t,0,1,0,1,0)
the Blanchfield form on it
3t^-1-4+3t
103
First homology
of the double branched cover of 12n_0086
Z/103
-2 2
12n_0087
1

detected by
an unknotting move
4-12t+17t^2-12t^3+4t^4
Seifert matrix of 12n_0087
-2 -1 -4 -4
-2 -2 -2 -3
-3 0 -5 -5
-4 -1 -6 -6
1
Generator of the Alexander module
(1,2,0,1)
the Blanchfield form on it
3t^-1-4+3t
49
First homology
of the double branched cover of 12n_0087
Z/49
0 0
12n_0088
3

detected by
the signature
4-14t+26t^2-31t^3+26t^4-14t^5+4t^6
Seifert matrix of 12n_0088
-1 -1 0 -1 -1 -1
0 -2 0 -1 -1 -1
0 0 -1 -1 -1 -1
0 -1 0 -2 -1 -2
0 -1 0 -1 -2 -1
0 -1 0 -1 -1 -2
1
Generator of the Alexander module
(1+2t-2t^3+2t^4-2t^5,0,2t^3-2t^4,0,2t^3-2t^4,0)
the Blanchfield form on it
12t^-2-24t^-1+31-24t+12t^2
119
First homology
of the double branched cover of 12n_0088
Z/119
-6 6
12n_0089
3

detected by
the signature
1-4t+6t^2-7t^3+7t^4-7t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0089
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
43
First homology
of the double branched cover of 12n_0089
Z/43
-6 6
12n_0090
2

detected by
the signature
-1+4t-10t^2+15t^3-17t^4+15t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0090
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 1 0 0 0 0
-1 -1 0 -1 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,t,2t,1,t,t,0,t)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
77
First homology
of the double branched cover of 12n_0090
Z/77
4 4
12n_0091
3

detected by
the signature
-1+6t^2-15t^3+19t^4-15t^5+6t^6-t^8
Seifert matrix of 12n_0091
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,t^2+t^3+t^5,-t+t^2+t^3+t^5,1+t^2+t^4,-t-t^2-t^3-t^4,1+t^2,-2t-2t^3,1-3t+2t^2-2t^3-t^4)
the Blanchfield form on it
x
59
First homology
of the double branched cover of 12n_0091
Z/59
-6 6
12n_0092
1

detected by
an unknotting move
-1+4t-12t^2+23t^3-29t^4+23t^5-12t^6+4t^7-t^8
Seifert matrix of 12n_0092
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
-1 -1 0 -1 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+10t^-1-13+10t-4t^2+t^3
109
First homology
of the double branched cover of 12n_0092
Z/109
0 0
12n_0093
3

detected by
the signature
1-4t+4t^2+t^3-5t^4+t^5+4t^6-4t^7+t^8
Seifert matrix of 12n_0093
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,1,-t,1)
the Blanchfield form on it
t^-3-6t^-2+13t^-1-17+13t-6t^2+t^3
11
First homology
of the double branched cover of 12n_0093
Z/11
-6 6
12n_0094
2

detected by
the signature
-2+9t-16t^2+19t^3-16t^4+9t^5-2t^6
Seifert matrix of 12n_0094
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 1 0 0
0 0 0 0 -1 1
1 1 0 1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
73
First homology
of the double branched cover of 12n_0094
Z/73
-4 4
12n_0095
2

detected by
the Lickorish test
2-9t+22t^2-29t^3+22t^4-9t^5+2t^6
Seifert matrix of 12n_0095
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 1 0 0
0 0 0 0 1 0
1 1 0 1 -1 2
1
Generator of the Alexander module
(0,t,1+t,0,0,-1-t)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
95
First homology
of the double branched cover of 12n_0095
Z/95
2 2
12n_0096
3

detected by
the signature
2-3t+3t^3-3t^5+2t^6
Seifert matrix of 12n_0096
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 -1 1
1 1 0 1 0 -2
1
Generator of the Alexander module
(0,0,1,0,1-2t,0)
the Blanchfield form on it
2t^-2-1+2t^2
7
First homology
of the double branched cover of 12n_0096
Z/7
-6 6
12n_0097
1

detected by
an unknotting move
-1+5t-9t^2+11t^3-9t^4+5t^5-t^6
Seifert matrix of 12n_0097
-1 -1 -1 -1 0 0
0 0 -1 -1 0 0
0 -1 0 -1 0 0
0 0 -1 0 0 0
0 1 0 1 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,-1)
the Blanchfield form on it
-t^-2+2t^-1-3+2t-t^2
41
First homology
of the double branched cover of 12n_0097
Z/41
0 2
12n_0098
2

detected by
the signature
-1+6t-14t^2+17t^3-17t^4+17t^5-14t^6+6t^7-t^8
Seifert matrix of 12n_0098
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 0
0 0 -1 1 0 -1 -1 1
0 0 -1 0 -1 0 -1 0
0 0 0 0 0 -1 0 0
-1 -1 0 0 0 0 -1 0
0 0 -1 0 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
93
First homology
of the double branched cover of 12n_0098
Z/93
-4 4
12n_0099
2

detected by
the Lickorish test
2-12t+32t^2-43t^3+32t^4-12t^5+2t^6
Seifert matrix of 12n_0099
-1 0 1 1 1 0
0 -1 0 0 0 0
0 -2 -6 -3 -3 -4
0 -1 -3 -2 -2 -2
0 -1 -2 -1 0 -1
0 -1 -4 -2 -2 -2
1
Generator of the Alexander module
(3-3t,0,0,0,-t,1)
the Blanchfield form on it
-9t^-2+34t^-1-49+34t-9t^2
135
First homology
of the double branched cover of 12n_0099
Z/135
-2 2
12n_0100
3

detected by
the signature
5-15t+23t^2-25t^3+23t^4-15t^5+5t^6
Seifert matrix of 12n_0100
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 1 1 1
1 1 0 -2 -1 -1
1 1 0 -1 -2 -1
1 1 0 0 -1 -2
1 or 2
111
First homology
of the double branched cover of 12n_0100
Z/111
-6 6
12n_0101
1

detected by
an unknotting move
-1+12t-34t^2+47t^3-34t^4+12t^5-t^6
Seifert matrix of 12n_0101
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 1 1 1
1 1 0 1 0 -1
1 1 0 0 1 0
1 1 0 0 0 1
1 or 2
141
First homology
of the double branched cover of 12n_0101
Z/141
0 0
12n_0102
2

detected by
the signature
-1+4t-4t^2+3t^3-4t^4+4t^5-t^6
Seifert matrix of 12n_0102
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 -1 -1 0 0
1 1 -1 0 -1 0
1 1 -1 1 0 -1
1 or 2
21
First homology
of the double branched cover of 12n_0102
Z/21
-4 4
12n_0103
3

detected by
the signature
1-4t+6t^2-8t^3+9t^4-8t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0103
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
47
First homology
of the double branched cover of 12n_0103
Z/47
-6 6
12n_0104
2

detected by
the signature
-1+4t-10t^2+14t^3-15t^4+14t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0104
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 0 1 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
73
First homology
of the double branched cover of 12n_0104
Z/73
4 4
12n_0105
3

detected by
the signature
-1+4t^2-8t^3+9t^4-8t^5+4t^6-t^8
Seifert matrix of 12n_0105
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,-t,1,-t,-t)
the Blanchfield form on it
-t^-3+4t^-1-7+4t-t^3
31
First homology
of the double branched cover of 12n_0105
Z/31
-6 6
12n_0106
1

detected by
an unknotting move
-1+4t-10t^2+16t^3-19t^4+16t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0106
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 0 1 0 1 1
1
Generator of the Alexander module
(0,0,1+t-t^2,0,1+t^2-t^3,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+7t^-1-9+7t-3t^2+t^3
81
First homology
of the double branched cover of 12n_0106
Z/81
0 0
12n_0107
3

detected by
the signature
1-4t+6t^2-6t^3+5t^4-6t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0107
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,-1-t^2,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+3t^-1-3+3t-3t^2+t^3
39
First homology
of the double branched cover of 12n_0107
Z/39
-6 6
12n_0108
2

detected by
the signature
-2+9t-15t^2+17t^3-15t^4+9t^5-2t^6
Seifert matrix of 12n_0108
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 1 0 0
0 0 0 0 -2 1
-1 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-10+9t-5t^2+t^3
69
First homology
of the double branched cover of 12n_0108
Z/69
-4 4
12n_0109
2

detected by
the Lickorish test
2-9t+23t^2-31t^3+23t^4-9t^5+2t^6
Seifert matrix of 12n_0109
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 1 0 0
0 0 0 0 2 0
-1 -1 0 -1 -1 1
1
Generator of the Alexander module
(0,0,-t,0,1,t)
the Blanchfield form on it
-t^-2+3t^-1-6+3t-t^2
99
First homology
of the double branched cover of 12n_0109
Z/99
2 2
12n_0110
2

detected by
the signature
2-t-7t^2+13t^3-7t^4-t^5+2t^6
Seifert matrix of 12n_0110
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 -2 1
-1 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,-1,0,1-2t,0)
the Blanchfield form on it
t^-2+t^-1-2+t+t^2
21
First homology
of the double branched cover of 12n_0110
Z/21
-4 4
12n_0111
1

detected by
an unknotting move
2-9t+21t^2-27t^3+21t^4-9t^5+2t^6
Seifert matrix of 12n_0111
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 2 0
-1 -1 0 -1 -1 1
1
Generator of the Alexander module
(0,t,t+t^2,0,1+t,t+t^2)
the Blanchfield form on it
2t^-2-7t^-1+11-7t+2t^2
91
First homology
of the double branched cover of 12n_0111
Z/91
-2 2
12n_0112
2

detected by
the signature
-2+9t-17t^2+21t^3-17t^4+9t^5-2t^6
Seifert matrix of 12n_0112
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 -2 1
-1 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-14+11t-5t^2+t^3
77
First homology
of the double branched cover of 12n_0112
Z/77
-4 4
12n_0113
2

detected by
the signature
1-3t+7t^2-10t^3+11t^4-10t^5+7t^6-3t^7+t^8
Seifert matrix of 12n_0113
-1 -1 -1 0 0 -1 0 0
0 0 -1 1 1 -1 1 1
0 -1 0 0 0 -1 0 0
0 0 0 1 0 0 1 0
0 0 0 1 1 0 1 1
0 0 -1 1 1 0 1 1
0 0 0 0 0 0 1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(-1+t,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
53
First homology
of the double branched cover of 12n_0113
Z/53
4 4
12n_0114
3

detected by
the signature
1-5t+9t^2-12t^3+13t^4-12t^5+9t^6-5t^7+t^8
Seifert matrix of 12n_0114
-1 -1 -1 0 0 -1 0 0
0 -2 -1 0 0 -2 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 -1 -1 -1 0 -1
0 -1 0 0 -1 -1 0 0
0 -1 -1 0 0 -2 0 0
0 -1 0 -1 -1 -1 -1 -1
0 -1 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-11+9t-5t^2+t^3
67
First homology
of the double branched cover of 12n_0114
Z/67
-6 6
12n_0115
1

detected by
an unknotting move
1-t-t^2+4t^3-5t^4+4t^5-t^6-t^7+t^8
Seifert matrix of 12n_0115
-1 -1 -1 0 0 -1 0 0
0 0 -1 1 1 -1 1 1
0 -1 -2 0 0 -1 0 0
0 0 0 1 0 0 1 0
0 0 0 1 1 0 1 1
0 0 -1 1 1 0 1 1
0 0 0 0 0 0 1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(t,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-1-2+t
11
First homology
of the double branched cover of 12n_0115
Z/11
2 2
12n_0116
1

detected by
an unknotting move
2-7t+16t^2-21t^3+16t^4-7t^5+2t^6
Seifert matrix of 12n_0116
-1 -1 -1 0 0 -1
0 0 -1 -1 1 -1
0 -1 0 0 0 -1
0 0 0 2 0 0
0 0 0 -1 1 0
0 0 -1 -1 1 0
1
Generator of the Alexander module
(-2+t-t^2,0,-t^2,1+t,-t,t)
the Blanchfield form on it
2t^-2-7t^-1+10-7t+2t^2
71
First homology
of the double branched cover of 12n_0116
Z/71
2 2
12n_0117
2

detected by
the signature
-2+11t-22t^2+27t^3-22t^4+11t^5-2t^6
Seifert matrix of 12n_0117
-1 -1 -1 0 0 -1
0 -2 -1 0 0 -2
0 -1 0 0 0 -1
0 1 0 -2 1 1
0 -1 0 0 -1 -1
0 -1 -1 0 0 -2
1
Generator of the Alexander module
(-4+3t-24t^2-23t^3-32t^4+19t^5-10t^6+40t^7,0,-20t^2-54t^3-58t^4-50t^5-40t^6,1+8t+5t^2+11t^3+16t^4+64t^5+20t^6+80t^7,4t+9t^2+20t^3+21t^4+20t^5,4+13t+17t^2+9t^3+20t^4)
the Blanchfield form on it
x
97
First homology
of the double branched cover of 12n_0117
Z/97
-4 4
12n_0118
1

detected by
an unknotting move
2-3t+3t^3-3t^5+2t^6
Seifert matrix of 12n_0118
-1 -1 -1 0 0 -1
0 0 -1 -1 1 -1
0 -1 -2 0 0 -1
0 0 0 2 0 0
0 0 0 -1 1 0
0 0 -1 -1 1 0
1
Generator of the Alexander module
(t,0,-t,1,0,0)
the Blanchfield form on it
2t^-2+t^-1-4+t+2t^2
7
First homology
of the double branched cover of 12n_0118
Z/7
2 2
12n_0119
2

detected by
the signature
-1+3t-3t^2+3t^3-3t^4+3t^5-t^6
Seifert matrix of 12n_0119
-1 -1 0 -1 0 0
0 0 0 -1 0 0
0 0 -1 -1 0 0
0 -1 0 0 0 0
0 0 0 1 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
17
First homology
of the double branched cover of 12n_0119
Z/17
-4 4
12n_0120
1

detected by
an unknotting move
1-2t+4t^2-5t^3+4t^4-2t^5+t^6
Seifert matrix of 12n_0120
-1 -1 0 1 0 0
0 0 0 1 0 0
0 0 1 0 0 1
0 1 -1 1 1 -1
0 0 0 0 1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(-1,0,0,2,0,0)
the Blanchfield form on it
t^-2-5t^-1+7-5t+t^2
19
First homology
of the double branched cover of 12n_0120
Z/19
2 2
12n_0121
1

detected by
an unknotting move
1-t^2+t^4
Seifert matrix of 12n_0121
-1 -1 0 -1
0 0 0 -1
0 0 1 0
0 -1 -1 2
1
Generator of the Alexander module
(1,0,0,1)
the Blanchfield form on it
t^-1-2+t
1
First homology
of the double branched cover of 12n_0121
0
0 2
12n_0122
1

detected by
an unknotting move
1-6t+14t^2-21t^3+23t^4-21t^5+14t^6-6t^7+t^8
Seifert matrix of 12n_0122
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 1 0 0
0 0 -1 -1 0 0 -1 0
0 0 0 0 1 0 -1 0
0 0 0 0 0 1 0 1
-1 -1 -1 0 0 1 -1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,t+2t^2,0,-1-t,t+t^2,-1-t,0,0)
the Blanchfield form on it
t^-3-6t^-2+14t^-1-19+14t-6t^2+t^3
107
First homology
of the double branched cover of 12n_0122
Z/107
-2 2
12n_0123
2

detected by
the signature
-2+14t-34t^2+45t^3-34t^4+14t^5-2t^6
Seifert matrix of 12n_0123
-2 -1 0 -1 -1 0
-2 -2 0 -1 -1 0
1 1 0 0 0 1
-1 -1 -1 -2 -1 0
-1 -1 0 -1 -2 0
-1 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-4t^-2+13t^-1-18+13t-4t^2
145
First homology
of the double branched cover of 12n_0123
Z/145
-4 4
12n_0124
1

detected by
an unknotting move
2-3t+2t^2
Seifert matrix of 12n_0124
1 1
0 2
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
-1
7
First homology
of the double branched cover of 12n_0124
Z/7
2 2
12n_0125
2

detected by
the signature
-1+6t-14t^2+17t^3-17t^4+17t^5-14t^6+6t^7-t^8
Seifert matrix of 12n_0125
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 1
0 0 -1 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
-1 -1 -1 0 1 0 -1 1
0 0 0 0 1 -1 0 1
1
Generator of the Alexander module
(0,0,-t,-t,1,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+4t^-1-4+4t-4t^2+t^3
93
First homology
of the double branched cover of 12n_0125
Z/93
-4 4
12n_0126
2

detected by
the Lickorish test
2-12t+32t^2-43t^3+32t^4-12t^5+2t^6
Seifert matrix of 12n_0126
-2 -1 0 -1 -1 1
-2 -2 0 -1 -1 1
0 0 0 -1 -1 0
-1 -1 -1 -2 -1 1
0 0 0 0 -1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(-3+2t-3t^2+2t^3,0,-4-7t+6t^2,-2-2t+2t^2,2+2t-2t^2,0)
the Blanchfield form on it
288t^-2-1102t^-1+1623-1102t+288t^2
135
First homology
of the double branched cover of 12n_0126
Z/135
-2 2
12n_0127
1

detected by
an unknotting move
1-6t+14t^2-21t^3+23t^4-21t^5+14t^6-6t^7+t^8
Seifert matrix of 12n_0127
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 -1
0 0 -1 1 0 1 0 -1
0 0 -1 0 -1 0 0 -1
0 0 -1 0 0 1 0 0
0 0 0 0 0 0 1 -1
-1 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,t,1,-1,0,1)
the Blanchfield form on it
-t^-3+4t^-2-6t^-1+6-6t+4t^2-t^3
107
First homology
of the double branched cover of 12n_0127
Z/107
-2 2
12n_0128
2

detected by
the signature
-2+14t-34t^2+45t^3-34t^4+14t^5-2t^6
Seifert matrix of 12n_0128
-2 -1 0 0 0 0
-2 -2 0 0 0 0
0 0 2 1 0 0
0 0 1 0 0 0
0 0 1 1 -1 0
-1 -1 -2 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,2,-1)
the Blanchfield form on it
-2t^-2+10t^-1-14+10t-2t^2
145
First homology
of the double branched cover of 12n_0128
Z/145
-4 4
12n_0129
1

detected by
an unknotting move
2-3t+2t^2
Seifert matrix of 12n_0129
4 9
10 23
1
Generator of the Alexander module
(1,3)
the Blanchfield form on it
-1
7
First homology
of the double branched cover of 12n_0129
Z/7
2 2
12n_0130
2

detected by
the Lickorish test
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 12n_0130
-1 -1 -1 -1 0 -1
0 0 -1 -1 0 -1
0 -1 0 0 0 -1
0 -1 -1 0 0 -1
0 0 -1 -1 -1 -1
0 -1 -1 -1 0 0
1
Generator of the Alexander module
(1,0,0,0,-2+t,0)
the Blanchfield form on it
2t^-1-3+2t
65
First homology
of the double branched cover of 12n_0130
Z/65
0 2
12n_0131
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 12n_0131
-1 -1 -1 -1 0 -1
0 0 -1 -1 0 -1
0 -1 -2 -1 0 -1
0 -1 -2 -2 0 -1
0 0 -1 -1 1 -1
0 -1 -1 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,2-t,0)
the Blanchfield form on it
-2t^-1+3-2t
103
First homology
of the double branched cover of 12n_0131
Z/103
-2 2
12n_0132
1

detected by
an unknotting move
4-12t+17t^2-12t^3+4t^4
Seifert matrix of 12n_0132
-5 0 -3 -5
-2 -2 -2 -3
-4 -1 -2 -4
-6 -1 -4 -6
1
Generator of the Alexander module
(0,2,1,1)
the Blanchfield form on it
3t^-1-4+3t
49
First homology
of the double branched cover of 12n_0132
Z/49
0 0
12n_0133
3

detected by
the signature
4-14t+26t^2-31t^3+26t^4-14t^5+4t^6
Seifert matrix of 12n_0133
-1 -1 -1 -1 0 -1
0 -2 -1 -1 0 -1
0 -1 -2 -1 0 -1
0 -1 -2 -2 0 -1
0 0 -1 -1 -1 -1
0 -1 -1 -1 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-3t^-3+12t^-2-23t^-1+28-23t+12t^2-3t^3
119
First homology
of the double branched cover of 12n_0133
Z/119
-6 6
12n_0134
3

detected by
the signature
1-4t+6t^2-7t^3+7t^4-7t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0134
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,-1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
43
First homology
of the double branched cover of 12n_0134
Z/43
-6 6
12n_0135
2

detected by
the signature
-1+4t-10t^2+15t^3-17t^4+15t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0135
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
77
First homology
of the double branched cover of 12n_0135
Z/77
4 4
12n_0136
3

detected by
the signature
-1+6t^2-15t^3+19t^4-15t^5+6t^6-t^8
Seifert matrix of 12n_0136
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,t^2,1+t^2,t,-t^2,t+t^2,-t,0)
the Blanchfield form on it
-t^-3-t^-2+3t^-1-5+3t-t^2-t^3
59
First homology
of the double branched cover of 12n_0136
Z/59
-6 6
12n_0137
1

detected by
an unknotting move
-1+4t-12t^2+23t^3-29t^4+23t^5-12t^6+4t^7-t^8
Seifert matrix of 12n_0137
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,-1+t-2t^2+t^3,0,0,-2+2t^4-t^5,0,0)
the Blanchfield form on it
109
First homology
of the double branched cover of 12n_0137
Z/109
0 0
12n_0138
3

detected by
the signature
1-4t+4t^2+t^3-5t^4+t^5+4t^6-4t^7+t^8
Seifert matrix of 12n_0138
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-3-6t^-2+13t^-1-17+13t-6t^2+t^3
11
First homology
of the double branched cover of 12n_0138
Z/11
-6 6
12n_0139
2

detected by
the signature
-1+5t-11t^2+12t^3-11t^4+12t^5-11t^6+5t^7-t^8
Seifert matrix of 12n_0139
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 -1
-1 -1 0 -1 0 0 1 0
0 0 -1 -1 -1 0 0 -1
0 0 -1 0 0 1 0 -1
0 0 0 0 0 0 1 0
-1 -1 0 -1 0 0 1 -1
1 or 2
69
First homology
of the double branched cover of 12n_0139
Z/69
-4 4
12n_0140
1

detected by
an unknotting move
1-9t+27t^2-37t^3+27t^4-9t^5+t^6
Seifert matrix of 12n_0140
-2 -1 0 -1 0 1
-2 -2 0 -1 0 1
0 0 2 -1 1 2
-1 -1 0 0 0 1
0 0 1 0 0 1
0 0 0 0 0 -1
1
Generator of the Alexander module
(1,1,2,0,0,0)
the Blanchfield form on it
-t^-1+2-t
111
First homology
of the double branched cover of 12n_0140
Z/111
-2 2
12n_0141
1

detected by
an unknotting move
-1+5t-13t^2+19t^3-13t^4+5t^5-t^6
Seifert matrix of 12n_0141
-2 -1 -1 -1 0 -1
-2 -2 -1 -1 0 -1
0 0 -1 0 0 -1
-1 -1 -1 0 0 -1
1 1 0 1 1 1
-1 -1 -1 -1 0 0
1
Generator of the Alexander module
(0,0,2,0,1,2)
the Blanchfield form on it
-3t^-2+8t^-1-7+8t-3t^2
57
First homology
of the double branched cover of 12n_0141
Z/57
0 0
12n_0142
1

detected by
an unknotting move
1-5t+10t^2-11t^3+10t^4-5t^5+t^6
Seifert matrix of 12n_0142
2 1 0 0 -1 0
1 0 0 0 -1 0
0 1 -1 0 0 1
1 1 0 1 -1 1
0 0 0 0 -1 0
1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-10t^-1+17-10t+2t^2
43
First homology
of the double branched cover of 12n_0142
Z/43
-2 2
12n_0143
2

detected by
the signature
-1+3t-2t^2+t^3-2t^4+3t^5-t^6
Seifert matrix of 12n_0143
-1 0 0 0 0 -1
0 0 0 -1 -1 0
0 1 -1 1 0 0
0 -1 0 0 0 0
0 0 0 0 -1 0
0 0 0 1 0 -1
1
Generator of the Alexander module
(1,0,-t,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
13
First homology
of the double branched cover of 12n_0143
Z/13
-4 4
12n_0144
2

detected by
the Lickorish test
1-7t+18t^2-23t^3+18t^4-7t^5+t^6
Seifert matrix of 12n_0144
2 1 0 0 1 0
1 0 0 0 1 0
0 1 1 0 0 1
1 1 0 1 1 1
0 0 0 0 1 0
1 0 0 0 1 -1
2
75
First homology
of the double branched cover of 12n_0144
Z/75
2 2
12n_0145
2

detected by
the Lickorish test
1-6t+11t^2-6t^3+t^4
Seifert matrix of 12n_0145
3 2 0 1
2 1 0 1
0 1 1 1
2 1 0 0
2
25
First homology
of the double branched cover of 12n_0145
Z/25
0 0
12n_0146
1

detected by
an unknotting move
-2+12t-19t^2+12t^3-2t^4
Seifert matrix of 12n_0146
0 -1 0 0
0 5 2 0
1 3 2 1
0 0 0 1
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
-1
47
First homology
of the double branched cover of 12n_0146
Z/47
2 2
12n_0147
3

detected by
the new u==2 criterion
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 12n_0147
-1 0 0 0 0 -1
0 2 0 0 0 0
0 0 -1 0 -1 0
0 1 0 1 0 0
0 1 0 0 -1 0
0 -1 0 0 -1 -1
2
75
First homology
of the double branched cover of 12n_0147
Z/15+Z/5
-2 2
12n_0148
2

detected by
the signature
1+t-5t^2+7t^3-5t^4+t^5+t^6
Seifert matrix of 12n_0148
1 0 0 0 0 0
1 1 0 0 -1 0
0 0 1 0 1 0
1 0 0 1 0 0
1 0 0 0 1 0
0 0 1 0 1 1
1 or 2
17
First homology
of the double branched cover of 12n_0148
Z/17
4 4
12n_0149
2

detected by
the signature
2-t-t^2-t^3+2t^4
Seifert matrix of 12n_0149
1 0 0 0
1 1 1 0
-1 0 2 0
1 0 0 1
1
Generator of the Alexander module
(0,-t+t^2,1-t,1+t-t^2)
the Blanchfield form on it
11t^-2-6t^-1-6-6t+11t^2
5
First homology
of the double branched cover of 12n_0149
Z/5
4 4
12n_0150
2

detected by
the signature
-1+5t-10t^2+9t^3-7t^4+9t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0150
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 0
0 0 0 1 0 0 -1 0
0 0 0 0 -1 0 0 0
0 0 -1 0 0 -1 -1 0
-1 -1 0 0 0 0 -1 0
0 0 0 1 1 0 -1 1
1
Generator of the Alexander module
(0,-1+3t-t^2+2t^3-3t^4+2t^5,1-t+t^3,1-t^2+t^3,1+2t-3t^2+2t^3,-1-t^2-t^3+2t^4-2t^5,0,-1+t-4t^2+4t^3-2t^4)
the Blanchfield form on it
x
57
First homology
of the double branched cover of 12n_0150
Z/57
-4 4
12n_0151
2

detected by
the Lickorish test
1-8t+24t^2-33t^3+24t^4-8t^5+t^6
Seifert matrix of 12n_0151
-1 0 0 0 1 -1
0 -1 0 0 0 0
0 -1 -2 0 0 1
-1 0 0 -1 0 -1
0 0 0 0 1 0
0 0 1 0 0 0
1
Generator of the Alexander module
(0,0,1-3t+t^2,3-2t+3t^2-t^3,0,1-3t+t^2)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
99
First homology
of the double branched cover of 12n_0151
Z/99
-2 2
12n_0152
1

detected by
an unknotting move
-1+6t-16t^2+23t^3-16t^4+6t^5-t^6
Seifert matrix of 12n_0152
1 0 0 1 1 0
0 -1 0 0 0 0
0 -1 -2 -2 0 -1
0 -1 -1 0 0 -1
0 0 0 0 -1 0
0 -1 -1 -1 0 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-1
69
First homology
of the double branched cover of 12n_0152
Z/69
0 0
12n_0153
4

detected by
the signature
-2+4t-3t^2-t^3+3t^4-t^5-3t^6+4t^7-2t^8
Seifert matrix of 12n_0153
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 -1 1
-1 -1 0 -1 0 0 0 1
0 0 0 0 -1 0 0 -1
0 0 -1 -1 0 -1 -1 1
-1 -1 0 -1 0 0 -1 1
1 1 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+t^-2-1+t^2-t^3
13
First homology
of the double branched cover of 12n_0153
Z/13
-8 8
12n_0154
1

detected by
an unknotting move
2-6t+10t^2-11t^3+10t^4-6t^5+2t^6
Seifert matrix of 12n_0154
1 0 -1 0 1 0
0 -1 0 0 0 0
-1 -1 -2 1 0 1
1 0 1 0 0 0
0 0 0 0 1 0
1 0 1 -1 0 0
1
Generator of the Alexander module
(0,0,-1,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+7t^-1-8+7t-4t^2+t^3
47
First homology
of the double branched cover of 12n_0154
Z/47
2 2
12n_0155
2

detected by
the signature
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 12n_0155
-3 -2 -2 -2 0 -2
-3 -3 -2 -2 0 -2
-1 -1 -2 -2 0 -1
-1 -1 -1 -2 0 -1
-1 -1 -1 -1 -1 -1
-2 -2 -2 -2 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
89
First homology
of the double branched cover of 12n_0155
Z/89
-4 4
12n_0156
2

detected by
the signature
-1+5t-8t^2+3t^3+t^4+3t^5-8t^6+5t^7-t^8
Seifert matrix of 12n_0156
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 -1
0 0 0 1 0 0 -1 0
0 0 0 0 1 0 0 -1
0 0 -1 0 0 -1 -1 -1
-1 -1 0 0 0 0 -1 -1
-1 -1 0 0 0 0 0 -1
1 or 2
33
First homology
of the double branched cover of 12n_0156
Z/33
-4 4
12n_0157
2

detected by
the Lickorish test
1-6t+18t^2-25t^3+18t^4-6t^5+t^6
Seifert matrix of 12n_0157
0 0 1 0 0 0
0 -1 0 0 0 0
1 -1 -2 0 0 1
0 0 0 -1 0 -1
-1 0 0 0 -1 0
-1 0 1 0 0 0
1 or 2
75
First homology
of the double branched cover of 12n_0157
Z/75
-2 2
12n_0158
1

detected by
an unknotting move
-1+8t-22t^2+31t^3-22t^4+8t^5-t^6
Seifert matrix of 12n_0158
-2 -1 -1 0 0 -1
-2 -2 -1 0 0 -1
0 0 -1 0 0 0
1 1 1 1 1 1
-1 -1 -1 0 1 -1
-1 -1 -1 0 0 0
1
Generator of the Alexander module
(-t^2,t,0,-2-t^2,t^2,-1)
the Blanchfield form on it
57t^-2-220t^-1+314-220t+57t^2
93
First homology
of the double branched cover of 12n_0158
Z/93
0 0
12n_0159
1

detected by
an unknotting move
2-6t+12t^2-15t^3+12t^4-6t^5+2t^6
Seifert matrix of 12n_0159
-1 -1 -1 -1 1 0
0 0 -1 -1 1 0
0 -1 0 -1 1 0
0 0 -1 0 1 0
0 0 1 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
4t^-2-10t^-1+13-10t+4t^2
55
First homology
of the double branched cover of 12n_0159
Z/55
2 2
12n_0160
1

detected by
an unknotting move
-1+6t-12t^2+15t^3-12t^4+6t^5-t^6
Seifert matrix of 12n_0160
-1 -1 0 -1 -1 0
0 0 0 -1 -1 0
0 0 1 0 0 -1
0 -1 0 0 -1 0
0 0 0 -1 0 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-2t^-2+11t^-1-17+11t-2t^2
53
First homology
of the double branched cover of 12n_0160
Z/53
0 2
12n_0161
2

detected by
the Lickorish test
1-8t+22t^2-29t^3+22t^4-8t^5+t^6
Seifert matrix of 12n_0161
-1 -1 0 -1 -1 0
0 -2 0 -1 -2 0
0 0 -1 0 0 -1
0 -1 0 0 -1 0
0 -1 0 -1 -2 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(2-t,0,-3+t,0,0,0)
the Blanchfield form on it
-t^-2+5t^-1-6+5t-t^2
91
First homology
of the double branched cover of 12n_0161
Z/91
-2 2
12n_0162
1

detected by
an unknotting move
-1+6t-14t^2+19t^3-14t^4+6t^5-t^6
Seifert matrix of 12n_0162
-1 -1 0 -1 -1 0
0 0 0 -1 -1 0
0 0 1 0 0 -1
0 -1 0 -2 -1 0
0 0 0 -1 0 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-1+3-t
61
First homology
of the double branched cover of 12n_0162
Z/61
0 0
12n_0163
3

detected by
the signature
1-5t+8t^2-7t^3+5t^4-7t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0163
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 -1 0 0
0 0 -1 0 -1 -1 0 0
-1 -1 0 0 0 -1 0 0
0 0 0 -1 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-3-3t^-2+2t^-1-1+2t-3t^2+t^3
47
First homology
of the double branched cover of 12n_0163
Z/47
-6 6
12n_0164
2

detected by
the Lickorish test
-1+8t-20t^2+27t^3-20t^4+8t^5-t^6
Seifert matrix of 12n_0164
1 0 0 0 0 0
0 -1 0 0 0 0
0 -1 -2 0 1 0
0 0 0 -1 -1 0
0 0 1 0 0 0
1 0 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-2t^-1+3-2t
85
First homology
of the double branched cover of 12n_0164
Z/85
0 0
12n_0165
1

detected by
an unknotting move
1-6t+16t^2-21t^3+16t^4-6t^5+t^6
Seifert matrix of 12n_0165
-1 0 0 -1 0 0
0 -1 0 0 0 0
0 -1 -2 -4 -1 -2
0 -2 -2 -3 -2 -1
0 -1 -1 -2 0 -1
0 -1 -1 0 -1 0
1
Generator of the Alexander module
(-t,0,0,1,0,0)
the Blanchfield form on it
t^-2-4t^-1+7-4t+t^2
67
First homology
of the double branched cover of 12n_0165
Z/67
-2 2
12n_0166
4

detected by
the signature
-2+4t-5t^2+6t^3-7t^4+6t^5-5t^6+4t^7-2t^8
Seifert matrix of 12n_0166
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 0 -1 0 0 -1 0 1
0 0 0 0 -1 0 -1 -1
1 1 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+4t^-2-4t^-1+3-4t+4t^2-2t^3
41
First homology
of the double branched cover of 12n_0166
Z/41
-8 8
12n_0167
1

detected by
an unknotting move
3-9t+14t^2-15t^3+14t^4-9t^5+3t^6
Seifert matrix of 12n_0167
1 0 -1 1 1 1
0 -1 0 0 0 0
-1 -1 -2 0 0 0
0 0 0 1 0 0
0 0 0 1 1 1
0 0 0 1 0 1
1
Generator of the Alexander module
(-2+t,0,-3+2t,0,0,0)
the Blanchfield form on it
3t^-2-4t^-1+4-4t+3t^2
67
First homology
of the double branched cover of 12n_0167
Z/67
2 2
12n_0168
2

detected by
the signature
-1+5t-8t^2+9t^3-8t^4+5t^5-t^6
Seifert matrix of 12n_0168
-3 -2 0 0 0 -2
-3 -3 0 0 0 -2
0 0 -1 0 -1 0
0 0 -1 -1 -1 0
-1 -1 0 0 -1 -1
-2 -2 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
37
First homology
of the double branched cover of 12n_0168
Z/37
-4 4
12n_0169
3

detected by
the signature
4-9t+9t^2-7t^3+9t^4-9t^5+4t^6
Seifert matrix of 12n_0169
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 0 0 1
0 0 -1 -1 0 1
0 0 0 0 -2 0
1 1 0 0 -1 -2
1
Generator of the Alexander module
(0,-1,1+t,1,0,0)
the Blanchfield form on it
4t^-2-5t^-1+4-5t+4t^2
51
First homology
of the double branched cover of 12n_0169
Z/51
-6 6
12n_0170
1

detected by
an unknotting move
6-20t+29t^2-20t^3+6t^4
Seifert matrix of 12n_0170
1 0 -1 0
0 -1 0 0
-1 -1 -2 0
1 0 0 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
3t^-2-11t^-1+16-11t+3t^2
81
First homology
of the double branched cover of 12n_0170
Z/81
0 0
12n_0171
2

detected by
the Lickorish test
-2+10t-15t^2+10t^3-2t^4
Seifert matrix of 12n_0171
-9 -8 -4 -8
-9 -9 -4 -8
-3 -3 -2 -3
-8 -8 -4 -7
1
Generator of the Alexander module
(2,2,1,2)
the Blanchfield form on it
t^-2-5t^-1+8-5t+t^2
39
First homology
of the double branched cover of 12n_0171
Z/39
-2 2
12n_0172
3

detected by
the signature
1-5t+6t^2-t^3-3t^4-t^5+6t^6-5t^7+t^8
Seifert matrix of 12n_0172
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 -1 0
0 0 0 -1 0 0 0 0
-1 -1 0 0 -1 0 0 0
0 0 -1 0 -1 -1 -1 0
-1 -1 0 0 -1 0 -1 0
0 0 0 -1 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,1)
the Blanchfield form on it
-t^-3+t^-2-1+t^2-t^3
23
First homology
of the double branched cover of 12n_0172
Z/23
-6 6
12n_0173
2

detected by
the Lickorish test
1-6t+16t^2-25t^3+27t^4-25t^5+16t^6-6t^7+t^8
Seifert matrix of 12n_0173
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 -1 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 0 -1 -1 0
0 0 -1 0 1 0 -1 1
1
Generator of the Alexander module
(0,0,0,0,1+t,1+t,0,-t)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
123
First homology
of the double branched cover of 12n_0173
Z/123
-2 2
12n_0174
2

detected by
the Lickorish test
-1+6t-18t^2+35t^3-45t^4+35t^5-18t^6+6t^7-t^8
Seifert matrix of 12n_0174
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 1 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 -1 -1
-1 -1 1 -1 0 1 1 0
0 0 0 0 0 0 1 0
0 0 -1 0 0 0 -1 -1
1 or 2
165
First homology
of the double branched cover of 12n_0174
Z/165
0 0
12n_0175
1

detected by
an unknotting move
-1+4t-4t^2-5t^3+11t^4-5t^5-4t^6+4t^7-t^8
Seifert matrix of 12n_0175
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 -1 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 0 -1 -1 0
0 0 -1 0 1 0 -1 1
1
Generator of the Alexander module
(0,-4t-8t^3+13t^4-2t^5-3t^6+t^7,-4t-6t^2-14t^3+26t^4-4t^5-6t^6+2t^7,-2-3t-7t^2+13t^3-2t^4-3t^5+t^6,2+2t+7t^2-13t^3+15t^4-4t^5-11t^6+9t^7-2t^8,0,-1-3t-5t^2+2t^3+11t^4-9t^5+2t^6,1+t+t^2-10t^3-t^4+15t^5-10t^6+2t^7)
the Blanchfield form on it
x
3
First homology
of the double branched cover of 12n_0175
Z/3
-2 2
12n_0176
1

detected by
an unknotting move
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 12n_0176
-3 -2 -1 -2
-3 -3 -1 -2
-2 -2 0 -2
-2 -2 -1 -3
1 or 2
63
First homology
of the double branched cover of 12n_0176
Z/63
-2 2
12n_0177
3

detected by
the signature
4-11t+16t^2-17t^3+16t^4-11t^5+4t^6
Seifert matrix of 12n_0177
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 -1 1 1
1 1 0 0 -2 -1
1 1 0 0 0 -2
1 or 2
79
First homology
of the double branched cover of 12n_0177
Z/79
-6 6
12n_0178
1

detected by
an unknotting move
-1+9t-24t^2+33t^3-24t^4+9t^5-t^6
Seifert matrix of 12n_0178
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 -1 1 1
1 1 0 0 1 -1
1 1 1 0 0 1
1
Generator of the Alexander module
(-134-682t+922t^2+2030t^3-1238t^4-820t^5-1228t^6+1692t^7-980t^8-168t^9,67+341t-461t^2-1015t^3+619t^4+410t^5+614t^6-846t^7+490t^8+84t^9,0,-22-26t-135t^2+752t^3-533t^4+221t^5-618t^6+526t^7-224t^8-42t^9,23+135t-664t^2+457t^3-189t^4+624t^5-526t^6+224t^7+42t^8,88-163t-4t^2-1251t^3+2491t^4-1353t^5+910t^6-
the Blanchfield form on it
x
101
First homology
of the double branched cover of 12n_0178
Z/101
0 0
12n_0179
2

detected by
the signature
-1+3t-2t^2+t^3-2t^4+3t^5-t^6
Seifert matrix of 12n_0179
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 1 0 0
1 1 0 -1 -1 0
1 1 0 -1 1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
13
First homology
of the double branched cover of 12n_0179
Z/13
-4 4
12n_0180
1

detected by
an unknotting move
-2+10t-22t^2+29t^3-22t^4+10t^5-2t^6
Seifert matrix of 12n_0180
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
1 1 0 -1 -1 0
1 1 1 -1 1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
97
First homology
of the double branched cover of 12n_0180
Z/97
0 0
12n_0181
1

detected by
an unknotting move
2-9t+19t^2-23t^3+19t^4-9t^5+2t^6
Seifert matrix of 12n_0181
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 1 0 0
1 1 0 -1 2 0
1 1 0 -1 1 -1
1
Generator of the Alexander module
(0,0,1-2t,0,-2,0)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
83
First homology
of the double branched cover of 12n_0181
Z/83
-2 2
12n_0182
1

detected by
an unknotting move
1-5t+10t^2-13t^3+13t^4-13t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0182
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 1 0 -1
0 0 0 1 0 0 0 -1
0 0 -1 0 -1 0 0 -1
0 0 0 0 0 1 1 0
0 0 0 0 0 0 1 0
-1 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,t,0,1-t^2,0,-1,0,0)
the Blanchfield form on it
-2t^-3+4t^-2-5t^-1+4-5t+4t^2-2t^3
71
First homology
of the double branched cover of 12n_0182
Z/71
-2 2
12n_0183
2

detected by
the signature
-1+10t-26t^2+35t^3-26t^4+10t^5-t^6
Seifert matrix of 12n_0183
0 0 1 0 1 0
0 -1 0 0 0 0
1 -1 -2 0 -1 0
-1 0 0 -1 0 0
0 -1 -1 0 -2 0
0 0 0 0 1 -1
1 or 2
109
First homology
of the double branched cover of 12n_0183
Z/109
-4 4
12n_0184
1

detected by
an unknotting move
1-4t+10t^2-13t^3+10t^4-4t^5+t^6
Seifert matrix of 12n_0184
1 0 0 0 0 0
0 -1 0 0 0 0
0 -1 -2 -2 -1 1
0 -1 -1 0 -1 0
0 -1 -1 -1 0 0
1 0 0 0 0 1
1
Generator of the Alexander module
(0,1,1,0,1,0)
the Blanchfield form on it
2t^-2-5t^-1+6-5t+2t^2
43
First homology
of the double branched cover of 12n_0184
Z/43
2 2
12n_0185
3

detected by
the signature
1-4t+7t^2-10t^3+11t^4-10t^5+7t^6-4t^7+t^8
Seifert matrix of 12n_0185
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 0
-1 -1 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
-1 -1 0 -1 -1 -1 0 0
-1 -1 0 0 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-5+4t-3t^2+t^3
55
First homology
of the double branched cover of 12n_0185
Z/55
-6 6
12n_0186
2

detected by
the signature
-1+4t-11t^2+18t^3-21t^4+18t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0186
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 0 0
-1 -1 1 1 -1 1 0 0
0 0 0 0 1 0 0 0
-1 -1 1 0 -1 1 0 0
-1 -1 0 0 -1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+10t^-1-13+10t-4t^2+t^3
89
First homology
of the double branched cover of 12n_0186
Z/89
4 4
12n_0187
3

detected by
the signature
-1+5t^2-12t^3+15t^4-12t^5+5t^6-t^8
Seifert matrix of 12n_0187
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 0
-1 -1 0 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 0 -1 -1 -1 0 0
-1 -1 0 0 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,t,0,0,1,-t)
the Blanchfield form on it
-2t^-3-t^-2+11t^-1-18+11t-t^2-2t^3
47
First homology
of the double branched cover of 12n_0187
Z/47
-6 6
12n_0188
2

detected by
the signature
-1+4t-9t^2+12t^3-13t^4+12t^5-9t^6+4t^7-t^8
Seifert matrix of 12n_0188
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 0
-1 -1 0 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 0 -1 -1 -1 0 0
-1 -1 0 0 -1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-10t^-1+13-10t+4t^2-t^3
65
First homology
of the double branched cover of 12n_0188
Z/65
-4 4
12n_0189
1

detected by
an unknotting move
1-4t+9t^2-16t^3+19t^4-16t^5+9t^6-4t^7+t^8
Seifert matrix of 12n_0189
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 0 0
-1 -1 1 1 -1 1 0 0
0 0 0 0 -1 0 0 0
-1 -1 1 0 -1 1 0 0
-1 -1 0 0 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,-1,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-8+5t-3t^2+t^3
79
First homology
of the double branched cover of 12n_0189
Z/79
-2 2
12n_0190
2

detected by
the signature
1-3t+8t^2-13t^3+15t^4-13t^5+8t^6-3t^7+t^8
Seifert matrix of 12n_0190
-1 -1 -1 -1 0 -1 -1 0
0 0 -1 -1 1 -1 -1 1
0 0 0 -1 1 0 -1 1
0 -1 -1 0 0 -1 -1 0
0 0 0 0 1 0 0 1
0 0 -1 -1 1 0 -1 1
0 0 0 -1 1 0 0 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+3t^-2-7t^-1+9-7t+3t^2-t^3
65
First homology
of the double branched cover of 12n_0190
Z/65
4 4
12n_0191
3

detected by
the signature
1-5t+10t^2-15t^3+17t^4-15t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0191
-1 -1 -1 -1 0 -1 -1 0
0 -2 -2 -1 0 -2 -2 0
0 -1 -2 -1 0 -1 -2 0
0 -1 -1 0 0 -1 -1 0
0 -1 -1 0 -1 -1 -1 0
0 -1 -2 -1 0 -2 -2 0
0 -1 -1 -1 0 -1 -2 0
0 -1 -1 0 -1 -1 -1 -1
1
Generator of the Alexander module
(1,0,0,0,-2+2t-t^2,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+6t^-1-7+6t-4t^2+t^3
79
First homology
of the double branched cover of 12n_0191
Z/79
-6 6
12n_0192
1

detected by
an unknotting move
1-t-2t^2+7t^3-9t^4+7t^5-2t^6-t^7+t^8
Seifert matrix of 12n_0192
-1 -1 -1 -1 0 -1 -1 0
0 0 -1 -1 1 -1 -1 1
0 0 0 -1 1 0 -1 1
0 -1 -1 -2 0 -1 -1 0
0 0 0 0 1 0 0 1
0 0 -1 -1 1 0 -1 1
0 0 0 -1 1 0 0 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
23
First homology
of the double branched cover of 12n_0192
Z/23
2 2
12n_0193
1

detected by
an unknotting move
2-6t+13t^2-17t^3+13t^4-6t^5+2t^6
Seifert matrix of 12n_0193
-1 -1 1 -1 0 0
0 0 1 -1 1 1
0 0 1 1 -1 -1
0 -1 1 0 0 0
0 0 0 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+6t^-1-8+6t-3t^2+t^3
59
First homology
of the double branched cover of 12n_0193
Z/59
2 2
12n_0194
2

detected by
the signature
-2+10t-19t^2+23t^3-19t^4+10t^5-2t^6
Seifert matrix of 12n_0194
-1 -1 1 -1 0 0
0 -2 2 -1 0 0
0 1 -3 1 0 0
0 -1 1 0 0 0
0 -1 1 0 -1 0
0 -1 1 0 -1 -1
1
Generator of the Alexander module
(1+14t-6t^2-16t^3+7t^4,2+20t-10t^2-22t^3+10t^4,-1-6t+4t^2+6t^3-3t^4,3+t-23t^2+25t^3+23t^4-42t^5+12t^6,3-3t-14t^2+18t^3+10t^4-21t^5+6t^6,3-5t-22t^2+33t^3+20t^4-42t^5+12t^6)
the Blanchfield form on it
x
85
First homology
of the double branched cover of 12n_0194
Z/85
-4 4
12n_0195
1

detected by
an unknotting move
2-4t+3t^2-t^3+3t^4-4t^5+2t^6
Seifert matrix of 12n_0195
-1 -1 1 -1 0 0
0 0 1 -1 1 1
0 0 1 1 -1 -1
0 -1 1 -2 0 0
0 0 0 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(t,0,1,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-2t^-1-2t+3t^2-t^3
19
First homology
of the double branched cover of 12n_0195
Z/19
2 2
12n_0196
2

detected by
the signature
-2+6t-7t^2+7t^3-7t^4+6t^5-2t^6
Seifert matrix of 12n_0196
-1 -1 1 -1 0 0
0 -1 2 -1 0 0
0 1 0 1 0 0
0 -1 1 -2 0 0
0 -1 1 0 -1 0
0 -1 1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,-t,0,t)
the Blanchfield form on it
t^-2+t^2
37
First homology
of the double branched cover of 12n_0196
Z/37
-4 4
12n_0197
1

detected by
an unknotting move
2-10t+25t^2-33t^3+25t^4-10t^5+2t^6
Seifert matrix of 12n_0197
-1 -1 1 -1 0 0
0 -1 1 -1 1 1
0 0 -2 1 -1 -1
0 -1 1 -2 0 0
0 0 0 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(-t+t^4,-3t^4,-1+2t+t^4,1,0,0)
the Blanchfield form on it
-11t^-5+40t^-4-113t^-3+282t^-2-528t^-1+660-528t+282t^2-113t^3+40t^4-11t^5
107
First homology
of the double branched cover of 12n_0197
Z/107
-2 2
12n_0198
1

detected by
an unknotting move
1-4t+6t^2-5t^3+6t^4-4t^5+t^6
Seifert matrix of 12n_0198
-1 0 -1 0 0 -1
0 1 0 0 -1 0
0 0 0 0 0 -1
0 0 0 -1 0 -1
0 0 0 -1 -1 0
0 0 -1 0 0 0
1
Generator of the Alexander module
(0,t,0,0,1,0)
the Blanchfield form on it
t^-2-2t^-1+1-2t+t^2
27
First homology
of the double branched cover of 12n_0198
Z/27
-2 2
12n_0199
1

detected by
an unknotting move
1-t+2t^2-3t^3+2t^4-t^5+t^6
Seifert matrix of 12n_0199
-1 0 -1 1 0 0
0 1 0 0 1 0
0 0 0 1 0 0
0 1 1 1 1 1
0 0 0 0 1 0
0 1 0 0 1 1
1
Generator of the Alexander module
(-t,0,1,0,0,0)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
11
First homology
of the double branched cover of 12n_0199
Z/11
2 2
12n_0200 1 or 2
2-2t+t^2-2t^3+2t^4
Seifert matrix of 12n_0200
-1 0 -1 1
0 2 0 0
0 0 0 1
0 -1 1 1
1
Generator of the Alexander module
(-1,0,0,1)
the Blanchfield form on it
2t^-1-4+2t
9
First homology
of the double branched cover of 12n_0200
Z/9
0 2
12n_0201
2

detected by
the signature
-3+13t-23t^2+27t^3-23t^4+13t^5-3t^6
Seifert matrix of 12n_0201
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -2 0 -1 1
0 0 0 1 0 0
1 1 -1 1 -2 1
-1 -1 0 -1 0 -1
1 or 2
105
First homology
of the double branched cover of 12n_0201
Z/105
-4 4
12n_0202
2

detected by
the Lickorish test
3-13t+31t^2-41t^3+31t^4-13t^5+3t^6
Seifert matrix of 12n_0202
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 2 0 1 0
0 0 0 1 0 0
1 1 1 1 2 0
-1 -1 -1 -1 -1 1
1 or 2
135
First homology
of the double branched cover of 12n_0202
Z/135
2 2
12n_0203
3

detected by
the signature
3-5t+t^2+3t^3+t^4-5t^5+3t^6
Seifert matrix of 12n_0203
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -2 0 -1 1
0 0 0 -1 0 0
1 1 -1 1 -2 1
-1 -1 0 -1 0 -1
1 or 2
15
First homology
of the double branched cover of 12n_0203
Z/15
-6 6
12n_0204
2

detected by
the signature
-1+9t-22t^2+29t^3-22t^4+9t^5-t^6
Seifert matrix of 12n_0204
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 0
0 0 0 -1 0 0
1 1 0 1 -1 0
-1 -1 -1 -1 -1 1
1 or 2
93
First homology
of the double branched cover of 12n_0204
Z/93
-4 4
12n_0205
2

detected by
the signature
-1+5t-11t^2+14t^3-15t^4+14t^5-11t^6+5t^7-t^8
Seifert matrix of 12n_0205
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
0 0 0 1 0 0 0 0
0 0 -1 0 -1 -1 0 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 -1 -1 -1 0
0 0 -1 0 -1 0 0 1
1 or 2
77
First homology
of the double branched cover of 12n_0205
Z/77
-4 4
12n_0206
2

detected by
the Lickorish test
1-5t+13t^2-24t^3+29t^4-24t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0206
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 1 0 1 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 1 -1 1 1 1 0
0 0 0 0 0 0 1 0
0 0 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,1-3t+t^2+2t^3-7t^4-t^5+22t^6-50t^7+52t^8-12t^9-16t^10+11t^11-2t^12,2t+2t^2+2t^3-6t^4+18t^5-32t^6+44t^7-20t^8-18t^9+18t^10-4t^11,1+2t+4t^2-7t^3+10t^4-8t^5-6t^6+32t^7-30t^8+2t^9+7t^10-2t^11,-1-t^2-t^3-3t^4+20t^5-45t^6+72t^7-63t^8+14t^9+16t^10-11t^11+2t^12,t+2t^2+6t^3-12t^4+14t^5-9t^6-18t^7+52t^8-41
the Blanchfield form on it
x
115
First homology
of the double branched cover of 12n_0206
Z/115
2 2
12n_0207
2

detected by
the signature
1-3t-t^2+12t^3-19t^4+12t^5-t^6-3t^7+t^8
Seifert matrix of 12n_0207
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
0 0 0 -1 0 0 0 0
0 0 -1 0 -1 -1 0 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 -1 -1 -1 0
0 0 -1 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,1,0,1,0,0,t)
the Blanchfield form on it
t^-3-4t^-1+7-4t+t^3
37
First homology
of the double branched cover of 12n_0207
Z/37
-4 4
12n_0208
1

detected by
an unknotting move
3-11t+23t^2-29t^3+23t^4-11t^5+3t^6
Seifert matrix of 12n_0208
-1 -1 -1 -1 0 0
0 0 -1 -1 0 0
0 -1 0 -1 0 0
0 -1 -1 0 1 -1
0 0 0 0 1 0
0 1 0 0 -1 2
1
Generator of the Alexander module
(-1-t^2+t^3,0,0,t-t^2,-1+t,1-t)
the Blanchfield form on it
6t^-2-13t^-1+16-13t+6t^2
103
First homology
of the double branched cover of 12n_0208
Z/103
2 2
12n_0209
2

detected by
the signature
-3+15t-31t^2+39t^3-31t^4+15t^5-3t^6
Seifert matrix of 12n_0209
-1 -1 -1 -1 0 0
0 -2 -1 -1 0 -1
0 -1 0 -1 0 0
0 -1 -1 -2 0 0
0 0 0 -1 -1 1
0 0 0 1 0 -2
1
Generator of the Alexander module
(1-t+2t^2-t^3+t^4,0,-t+t^2-t^3,1,0,0)
the Blanchfield form on it
-6t^-2+15t^-1-20+15t-6t^2
137
First homology
of the double branched cover of 12n_0209
Z/137
-4 4
12n_0210
1

detected by
an unknotting move
1-t-t^2+3t^3-t^4-t^5+t^6
Seifert matrix of 12n_0210
-1 -1 -1 -1 0 0
0 0 -1 -1 0 0
0 -1 -2 -1 0 0
0 -1 -1 0 1 -1
0 0 0 0 1 0
0 1 0 0 -1 2
1
Generator of the Alexander module
(t^2,-2t,-t+2t^2+2t^4,1+t^2,-t,0)
the Blanchfield form on it
-5t^-2-18t^-1+25-18t-5t^2
1
First homology
of the double branched cover of 12n_0210
0
0 0
12n_0211
2

detected by
the Lickorish test
1-6t+12t^2-13t^3+12t^4-6t^5+t^6
Seifert matrix of 12n_0211
-1 -1 0 -1 0 -1
0 0 0 -1 0 -1
0 0 -1 -1 0 0
0 -1 0 0 0 -1
0 0 0 0 -1 -1
0 -1 0 0 0 0
1
Generator of the Alexander module
(0,0,0,0,-t,1)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
51
First homology
of the double branched cover of 12n_0211
Z/51
-2 2
12n_0212
1

detected by
an unknotting move
3-11t+23t^2-29t^3+23t^4-11t^5+3t^6
Seifert matrix of 12n_0212
-1 -1 -1 0 0 -1
0 0 -1 0 1 -1
0 -1 0 0 0 -1
0 1 0 2 1 0
0 0 0 0 1 0
0 -1 -1 -1 0 0
1
Generator of the Alexander module
(0,0,1-t,0,0,t)
the Blanchfield form on it
8t^-3-30t^-2+63t^-1-80+63t-30t^2+8t^3
103
First homology
of the double branched cover of 12n_0212
Z/103
2 2
12n_0213
2

detected by
the signature
-3+15t-31t^2+39t^3-31t^4+15t^5-3t^6
Seifert matrix of 12n_0213
-1 -1 -1 0 0 -1
0 -2 -1 -1 0 -1
0 -1 0 0 0 -1
0 0 0 -2 0 1
0 -1 0 -1 -1 0
0 -1 -1 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
137
First homology
of the double branched cover of 12n_0213
Z/137
-4 4
12n_0214
1

detected by
an unknotting move
1-t-t^2+3t^3-t^4-t^5+t^6
Seifert matrix of 12n_0214
-1 -1 -1 0 0 -1
0 0 -1 0 1 -1
0 -1 -2 0 0 -1
0 1 0 2 1 0
0 0 0 0 1 0
0 -1 -1 -1 0 0
1
Generator of the Alexander module
(-t,0,1,2t,-1,-t)
the Blanchfield form on it
-1
1
First homology
of the double branched cover of 12n_0214
0
0 0
12n_0215
2

detected by
the signature
-2+8t-13t^2+15t^3-13t^4+8t^5-2t^6
Seifert matrix of 12n_0215
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 1 -2 0 0
-1 -1 -1 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+7t^-1-8+7t-4t^2+t^3
61
First homology
of the double branched cover of 12n_0215
Z/61
-4 4
12n_0216
1

detected by
an unknotting move
2-8t+19t^2-25t^3+19t^4-8t^5+2t^6
Seifert matrix of 12n_0216
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 1 2 0 0
-1 -1 -1 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+9t^-1-12+9t-4t^2+t^3
83
First homology
of the double branched cover of 12n_0216
Z/83
2 2
12n_0217
2

detected by
the signature
2-2t-3t^2+7t^3-3t^4-2t^5+2t^6
Seifert matrix of 12n_0217
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 0
1 1 1 -2 0 0
-1 -1 -1 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+2t^-2-t^-1-t+2t^2-t^3
5
First homology
of the double branched cover of 12n_0217
Z/5
-4 4
12n_0218
1

detected by
an unknotting move
-1+4t-6t^2+7t^3-6t^4+4t^5-t^6
Seifert matrix of 12n_0218
-1 -1 0 0 0 -1
0 0 0 0 0 -1
0 0 -1 -1 0 -1
0 0 0 1 1 0
0 0 0 0 1 0
0 -1 0 0 0 0
1
Generator of the Alexander module
(t,0,1,0,0,0)
the Blanchfield form on it
-2t^-2+9t^-1-13+9t-2t^2
29
First homology
of the double branched cover of 12n_0218
Z/29
0 2
12n_0219
2

detected by
the Lickorish test
1-5t+12t^2-20t^3+23t^4-20t^5+12t^6-5t^7+t^8
Seifert matrix of 12n_0219
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 -1
0 0 0 1 0 0 0 -1
0 0 -1 0 1 0 1 -1
0 0 -1 0 0 -1 0 -1
0 0 -1 0 0 0 1 -1
-1 -1 0 0 0 0 0 -1
2
99
First homology
of the double branched cover of 12n_0219
Z/99
-2 2
12n_0220
2

detected by
the signature
1-3t+8t^3-13t^4+8t^5-3t^7+t^8
Seifert matrix of 12n_0220
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 -1
0 0 0 1 0 0 0 -1
0 0 -1 0 -1 0 0 -1
0 0 -1 0 0 -1 0 -1
0 0 -1 0 -1 0 -1 -1
-1 -1 0 0 0 0 0 -1
2
21
First homology
of the double branched cover of 12n_0220
Z/21
-4 4
12n_0221
2

detected by
A(F_2)
1-2t+3t^2-2t^3+t^4
Seifert matrix of 12n_0221
0 0 -1 -1
0 -2 1 0
0 1 0 0
-1 -1 1 0
2
9
First homology
of the double branched cover of 12n_0221
Z/9
0 0
12n_0222
2

detected by
the signature
-2+13t-30t^2+39t^3-30t^4+13t^5-2t^6
Seifert matrix of 12n_0222
-2 -1 0 0 0 0
-2 -2 0 0 0 0
0 0 2 0 1 0
-1 -1 -2 -1 -1 0
0 0 1 0 0 0
-1 -1 -1 0 0 -1
2
129
First homology
of the double branched cover of 12n_0222
Z/129
-4 4
12n_0223
2

detected by
the Lickorish test
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 12n_0223
-1 0 -1 0 -1 0
0 -1 0 0 0 0
0 -2 -6 -3 -3 -2
0 -1 -2 0 -1 -1
0 -1 -3 -1 -2 -1
0 -1 -2 -1 -1 0
2
111
First homology
of the double branched cover of 12n_0223
Z/111
-2 2
12n_0224
2

detected by
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0224
-1 -1 -1 -1 0 -1
0 0 -1 -1 0 -1
0 -1 0 -1 0 -1
0 0 -1 0 0 -1
0 0 0 0 -1 -1
0 -1 -1 -1 0 0
2
81
First homology
of the double branched cover of 12n_0224
Z/81
0 0
12n_0225
2

detected by
the Lickorish test
-3+10t-13t^2+10t^3-3t^4
Seifert matrix of 12n_0225
-2 -1 -2 -2
0 -2 -1 -2
-1 -1 -1 -2
-1 -1 -2 -3
2
39
First homology
of the double branched cover of 12n_0225
Z/39
-2 2
12n_0226
2

detected by
the signature
-1+5t-11t^2+14t^3-15t^4+14t^5-11t^6+5t^7-t^8
Seifert matrix of 12n_0226
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 -1
0 0 0 1 0 0 0 0
0 0 -1 0 1 0 -1 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 0 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1 or 2
77
First homology
of the double branched cover of 12n_0226
Z/77
-4 4
12n_0227
2

detected by
the Lickorish test
1-5t+13t^2-24t^3+29t^4-24t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0227
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 1 0
0 0 0 1 0 0 0 0
0 0 -1 0 -1 0 -1 0
-1 -1 1 -1 0 1 1 1
0 0 0 0 0 0 1 0
-1 -1 1 -1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+17-12t+5t^2-t^3
115
First homology
of the double branched cover of 12n_0227
Z/115
2 2
12n_0228
2

detected by
the signature
1-3t-t^2+12t^3-19t^4+12t^5-t^6-3t^7+t^8
Seifert matrix of 12n_0228
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 -1
0 0 0 -1 0 0 0 0
0 0 -1 0 1 0 -1 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 0 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-4t^-1+7-4t+t^3
37
First homology
of the double branched cover of 12n_0228
Z/37
-4 4
12n_0229
3

detected by
the signature
1-5t+8t^2-8t^3+7t^4-8t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0229
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 1 0
-1 -1 0 -1 0 0 1 0
0 0 -1 -1 -1 -1 0 0
-1 -1 0 -1 0 -1 1 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 -1
2
51
First homology
of the double branched cover of 12n_0229
Z/51
-6 6
12n_0230
1

detected by
an unknotting move
1-4t+4t^2-t^3+4t^4-4t^5+t^6
Seifert matrix of 12n_0230
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 -1 -1 0 0
0 0 0 -1 0 0
-1 0 0 -1 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1-3t+t^2,-6t+2t^2+2t^5-6t^6+2t^7,3t+11t^2-4t^3-t^5-t^6+11t^7-4t^8,-3-11t+4t^2+4t^5-12t^6+4t^7)
the Blanchfield form on it
x
19
First homology
of the double branched cover of 12n_0230
Z/19
-2 2
12n_0231
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 12n_0231
0 0 1 1
1 3 1 1
1 1 0 0
1 2 1 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-1
31
First homology
of the double branched cover of 12n_0231
Z/31
2 2
12n_0232
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 12n_0232
0 0 1 -1
0 2 0 0
1 -1 2 -1
0 0 0 1
1
Generator of the Alexander module
(1,0,-1+t,0)
the Blanchfield form on it
2t^-1-4+2t
31
First homology
of the double branched cover of 12n_0232
Z/31
2 2
12n_0233
2

detected by
the signature
1-2t+4t^2-5t^3+5t^4-5t^5+4t^6-2t^7+t^8
Seifert matrix of 12n_0233
-1 -1 -1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 -1 -1 -1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 -1 -1 -1 0 -1 -1 -1
0 0 -1 -1 -1 0 -1 -1
0 0 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 0
1
Generator of the Alexander module
(-t,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+2t^-1-2+2t-2t^2+t^3
29
First homology
of the double branched cover of 12n_0233
Z/29
4 4
12n_0234
3

detected by
the signature
1-4t+6t^2-7t^3+7t^4-7t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0234
-1 -1 -1 -1 -1 -1 -1 -1
0 -2 -2 -2 -1 -2 -2 -2
0 -1 -2 -2 -1 -1 -2 -2
0 -1 -1 -2 -1 -1 -1 -2
0 -1 -1 -1 0 -1 -1 -1
0 -1 -2 -2 -1 -2 -2 -2
0 -1 -1 -2 -1 -1 -2 -2
0 -1 -1 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(-t,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+2t^-1-2+2t-2t^2+t^3
43
First homology
of the double branched cover of 12n_0234
Z/43
-6 6
12n_0235
2

detected by
the signature
1-2t+2t^2-t^3+t^4-t^5+2t^6-2t^7+t^8
Seifert matrix of 12n_0235
-1 -1 -1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 -1 -1 -1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 -1 -1 -1 -2 -1 -1 -1
0 0 -1 -1 -1 0 -1 -1
0 0 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 0
1
Generator of the Alexander module
(t,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3+t^3
13
First homology
of the double branched cover of 12n_0235
Z/13
4 4
12n_0236
1

detected by
an unknotting move
2-5t+10t^2-13t^3+10t^4-5t^5+2t^6
Seifert matrix of 12n_0236
-1 -1 -1 1 -1 -1
0 0 -1 1 -1 -1
0 0 0 1 -1 0
0 0 0 1 1 0
0 -1 -1 1 0 -1
0 0 -1 1 -1 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
4t^-2-8t^-1+9-8t+4t^2
47
First homology
of the double branched cover of 12n_0236
Z/47
2 2
12n_0237
2

detected by
the signature
-2+9t-16t^2+19t^3-16t^4+9t^5-2t^6
Seifert matrix of 12n_0237
-1 -1 -1 1 -1 -1
0 -2 -2 2 -1 -2
0 -1 -2 2 -1 -1
0 1 1 -3 1 1
0 -1 -1 1 0 -1
0 -1 -2 2 -1 -2
1
Generator of the Alexander module
(t,0,0,-1,0,0)
the Blanchfield form on it
2t^-2-3t^-1+4-3t+2t^2
73
First homology
of the double branched cover of 12n_0237
Z/73
-4 4
12n_0238
1

detected by
an unknotting move
2-5t+6t^2-5t^3+6t^4-5t^5+2t^6
Seifert matrix of 12n_0238
-1 -1 -1 1 -1 -1
0 0 -1 1 -1 -1
0 0 0 1 -1 0
0 0 0 1 1 0
0 -1 -1 1 -2 -1
0 0 -1 1 -1 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
31
First homology
of the double branched cover of 12n_0238
Z/31
2 2
12n_0239
1

detected by
an unknotting move
2-5t+9t^2-11t^3+9t^4-5t^5+2t^6
Seifert matrix of 12n_0239
-1 -1 1 1 -1 1
0 0 1 1 -1 1
0 0 1 0 1 0
0 0 1 1 1 1
0 -1 1 1 0 1
0 0 1 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
4t^-2-9t^-1+11-9t+4t^2
43
First homology
of the double branched cover of 12n_0239
Z/43
2 2
12n_0240
2

detected by
the signature
-2+9t-17t^2+21t^3-17t^4+9t^5-2t^6
Seifert matrix of 12n_0240
-1 -1 1 1 -1 1
0 -2 2 2 -1 2
0 1 -3 -3 1 -3
0 1 -2 -3 1 -2
0 -1 1 1 0 1
0 1 -2 -3 1 -3
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
77
First homology
of the double branched cover of 12n_0240
Z/77
-4 4
12n_0241
1

detected by
an unknotting move
2-7t+13t^2-15t^3+13t^4-7t^5+2t^6
Seifert matrix of 12n_0241
-1 -1 1 1 -1 1
0 0 1 1 -1 1
0 0 1 0 1 0
0 0 1 1 1 1
0 -1 1 1 -2 1
0 0 1 0 1 1
1
Generator of the Alexander module
(2t,0,1,1,t,1)
the Blanchfield form on it
2t^-2-3t^-1+4-3t+2t^2
59
First homology
of the double branched cover of 12n_0241
Z/59
2 2
12n_0242
4

detected by
the signature
-1+t-t^3+t^4-t^5+t^6-t^7+t^9-t^10
Seifert matrix of 12n_0242
-1 0 0 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 -1 -1 -1
-1 -1 0 -1 -1 -1 0 0 -1 -1
-1 -1 0 0 -1 -1 0 0 0 -1
-1 -1 0 0 0 -1 0 0 0 0
0 0 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 -1 0 -1 -1 -1
-1 -1 0 0 -1 -1 0 0 -1 -1
-1 -1 0 0 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0,t,0,0,0)
the Blanchfield form on it
-t^-4-t^4
1
First homology
of the double branched cover of 12n_0242
0
-8 8
12n_0243
4

detected by
the signature
-2+3t-t^2-2t^3+3t^4-2t^5-t^6+3t^7-2t^8
Seifert matrix of 12n_0243
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 1 -1 0 -1
-1 -1 0 -1 1 -1 0 0
1 1 0 0 -2 1 0 0
-1 -1 0 0 0 -1 0 0
0 0 -1 -1 1 -1 -1 -1
-1 -1 0 -1 1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-4-2t^-3+t^-2+t^-1-2+t+t^2-2t^3+t^4
5
First homology
of the double branched cover of 12n_0243
Z/5
-8 8
12n_0244
4

detected by
the signature
-2+4t-4t^2+2t^3-t^4+2t^5-4t^6+4t^7-2t^8
Seifert matrix of 12n_0244
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 1 1 -1 0 1
1 1 0 -2 -2 1 0 -2
1 1 0 -1 -2 1 0 -1
-1 -1 0 0 0 -1 0 0
0 0 -1 1 1 -1 -1 1
1 1 0 -1 -2 1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+3t^-2-t^-1-1-t+3t^2-2t^3
25
First homology
of the double branched cover of 12n_0244
Z/25
-8 8
12n_0245
3

detected by
the signature
4-8t+6t^2-3t^3+6t^4-8t^5+4t^6
Seifert matrix of 12n_0245
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 1 0 1
1 1 0 -2 0 -1
0 0 -1 1 -1 1
1 1 0 0 0 -2
1 or 2
39
First homology
of the double branched cover of 12n_0245
Z/39
-6 6
12n_0246
1

detected by
an unknotting move
5-17t+25t^2-17t^3+5t^4
Seifert matrix of 12n_0246
1 0 -1 0
0 -1 0 0
-1 -1 -2 -1
-1 0 -1 1
1
Generator of the Alexander module
(0,0,3t-2t^2,1-4t+2t^2)
the Blanchfield form on it
-5t^-1+7-5t
69
First homology
of the double branched cover of 12n_0246
Z/69
0 0
12n_0247
2

detected by
the Lickorish test
-3+13t-19t^2+13t^3-3t^4
Seifert matrix of 12n_0247
-3 -2 2 -2
-3 -3 2 -2
1 1 -3 1
-2 -2 2 -1
1
Generator of the Alexander module
(-2-5t+10t^2-5t^3,-3-6t+12t^2-6t^3,1+2t-4t^2+2t^3,-2-4t+8t^2-4t^3)
the Blanchfield form on it
247t^-2-1076t^-1+1580-1076t+247t^2
51
First homology
of the double branched cover of 12n_0247
Z/51
-2 2
12n_0248
2

detected by
the Lickorish test
3-6t+7t^2-6t^3+3t^4
Seifert matrix of 12n_0248
-1 -1 -1 -1
0 0 -1 -1
0 -1 0 -1
0 0 -1 2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
6t^-1-11+6t
25
First homology
of the double branched cover of 12n_0248
Z/25
0 2
12n_0249
1

detected by
an unknotting move
-3+12t-17t^2+12t^3-3t^4
Seifert matrix of 12n_0249
-1 -1 -1 -1
0 -2 -1 -2
0 -1 0 -1
0 -1 -1 -4
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
47
First homology
of the double branched cover of 12n_0249
Z/47
-2 2
12n_0250
1

detected by
an unknotting move
3-10t+15t^2-10t^3+3t^4
Seifert matrix of 12n_0250
-1 -1 -1 -1
0 0 -1 -1
0 -1 -2 -1
0 0 -1 2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
1
41
First homology
of the double branched cover of 12n_0250
Z/41
0 0
12n_0251
3

detected by
the signature
3-5t+2t^2+t^3+2t^4-5t^5+3t^6
Seifert matrix of 12n_0251
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 -1
-1 -1 0 -1 0 0
0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -3
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+2t^-2-t^-1-t+2t^2-t^3
19
First homology
of the double branched cover of 12n_0251
Z/19
-6 6
12n_0252
1

detected by
an unknotting move
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 12n_0252
-1 -1 0 -1 0 -1
0 0 0 -1 1 -1
0 1 -1 0 1 1
0 -1 0 0 0 -1
0 0 0 0 1 0
0 -1 0 -1 0 0
1
Generator of the Alexander module
(-t,0,1,0,0,1)
the Blanchfield form on it
-4t^-2+16t^-1-24+16t-4t^2
89
First homology
of the double branched cover of 12n_0252
Z/89
0 2
12n_0253
2

detected by
the Lickorish test
2-6t+12t^2-15t^3+12t^4-6t^5+2t^6
Seifert matrix of 12n_0253
-1 -1 0 -1 0 -1
0 0 0 -1 1 -1
0 1 1 0 1 1
0 -1 0 0 0 -1
0 0 0 0 1 0
0 -1 0 -1 0 0
1
Generator of the Alexander module
(-t,0,1,0,0,1)
the Blanchfield form on it
2t^-1-4+2t
55
First homology
of the double branched cover of 12n_0253
Z/55
2 2
12n_0254
2

detected by
the signature
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 12n_0254
-1 -1 0 -1 0 -1
0 -2 0 -1 0 -1
0 1 -1 0 1 1
0 -1 0 0 0 -1
0 -1 0 0 -1 0
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
65
First homology
of the double branched cover of 12n_0254
Z/65
-4 4
12n_0255
1

detected by
an unknotting move
2-12t+30t^2-39t^3+30t^4-12t^5+2t^6
Seifert matrix of 12n_0255
-1 -1 0 -1 0 -1
0 -2 0 -1 0 -1
0 1 1 0 1 1
0 -1 0 0 0 -1
0 -1 0 0 -1 0
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
127
First homology
of the double branched cover of 12n_0255
Z/127
-2 2
12n_0256
2

detected by
the Lickorish test
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 12n_0256
-8 -6 -6 0
-8 -6 -6 -1
-7 -5 -5 0
-3 -3 -2 -2
1
Generator of the Alexander module
(0,4,0,3)
the Blanchfield form on it
-44t^-1+80-44t
25
First homology
of the double branched cover of 12n_0256
Z/25
0 0
12n_0257
2

detected by
the Nakanishi index
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 12n_0257
0 2 2 0
0 0 0 1
1 2 3 1
1 2 2 -1
2
25
First homology
of the double branched cover of 12n_0257
Z/5+Z/5
0 0
12n_0258
1

detected by
an unknotting move
-1+4t-5t^2+4t^3-t^4
Seifert matrix of 12n_0258
-1 1 0 -1
-1 -1 -2 0
-1 0 -1 -1
0 1 0 -2
1
Generator of the Alexander module
(0,2,1,0)
the Blanchfield form on it
1
15
First homology
of the double branched cover of 12n_0258
Z/15
-2 2
12n_0259
3

detected by
the signature
4-12t+20t^2-23t^3+20t^4-12t^5+4t^6
Seifert matrix of 12n_0259
-1 -1 0 -1 0 -1
0 -2 0 -1 0 -1
0 1 -1 0 1 1
0 -1 0 -2 0 -1
0 -1 0 0 -1 0
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
6t^-2-18t^-1+25-18t+6t^2
95
First homology
of the double branched cover of 12n_0259
Z/95
-6 6
12n_0260 1 or 2
3-5t+5t^2-5t^3+3t^4
Seifert matrix of 12n_0260
-1 1 -1 1
0 1 1 0
0 1 0 1
0 -1 1 1
1 or 2
21
First homology
of the double branched cover of 12n_0260
Z/21
0 2
12n_0261
2

detected by
the signature
-1+5t-10t^2+12t^3-13t^4+12t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0261
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 -1
0 0 0 1 0 0 0 -1
0 0 -1 0 -1 0 -1 -1
0 0 0 0 0 1 0 0
0 0 -1 0 0 0 -1 -1
-1 -1 0 0 0 -1 0 -1
2
69
First homology
of the double branched cover of 12n_0261
Z/69
-4 4
12n_0262
1

detected by
an unknotting move
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 12n_0262
-1 -1 0 0 -1 -1
0 0 0 0 -1 -1
0 1 -1 -1 0 0
0 0 0 1 0 0
0 -1 0 0 0 -1
0 -1 0 1 -1 0
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
89
First homology
of the double branched cover of 12n_0262
Z/89
0 2
12n_0263
1

detected by
an unknotting move
2-12t+30t^2-39t^3+30t^4-12t^5+2t^6
Seifert matrix of 12n_0263
-1 -1 0 0 -1 -1
0 -2 0 0 -1 -1
0 1 1 -1 0 0
0 0 0 -1 0 -1
0 -1 0 0 0 -1
0 -1 0 0 -1 -2
1
Generator of the Alexander module
(-1,0,1,0,0,0)
the Blanchfield form on it
-2t^-1+4-2t
127
First homology
of the double branched cover of 12n_0263
Z/127
-2 2
12n_0264
2

detected by
the Lickorish test
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 12n_0264
-2 -2 -1 0
-3 -4 -3 0
-2 -4 -3 1
0 0 0 1
1
Generator of the Alexander module
(1,1,0,0)
the Blanchfield form on it
-t^-2+3t^-1-4+3t-t^2
25
First homology
of the double branched cover of 12n_0264
Z/25
0 0
12n_0265
1

detected by
an unknotting move
2-8t+14t^2-15t^3+14t^4-8t^5+2t^6
Seifert matrix of 12n_0265
-1 -1 0 -1 -1 0
0 0 0 -1 -1 0
0 1 -1 0 1 0
0 -1 0 0 -1 0
0 -1 0 -1 0 0
0 0 -1 0 1 -1
1
Generator of the Alexander module
(1+5t+3t^3+4t^4-2t^5-3t^6+t^7,-6t-3t^2+2t^3-11t^4+4t^5+3t^6-t^7,-1+t-14t^2+19t^3-21t^4+9t^5-2t^6+9t^7-9t^8+2t^9,1+8t+2t^3+10t^4-7t^5-2t^6+t^7,-1-6t+16t^2-28t^3+27t^4-13t^5+12t^6-12t^7+9t^8-2t^9,-3t+12t^2-16t^3+35t^4-23t^5+20t^6-10t^7+7t^8-8t^9+2t^10)
the Blanchfield form on it
x
63
First homology
of the double branched cover of 12n_0265
Z/63
-2 2
12n_0266
2

detected by
the Lickorish test
-2+10t-24t^2+33t^3-24t^4+10t^5-2t^6
Seifert matrix of 12n_0266
-1 -1 0 -1 -1 0
0 -2 0 -1 -1 0
0 1 1 0 1 1
0 -1 0 0 -1 0
0 -1 0 -1 -2 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-6t^-1+7-6t+2t^2
105
First homology
of the double branched cover of 12n_0266
Z/105
0 0
12n_0267
2

detected by
the Lickorish test
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 12n_0267
-2 -5 -2 -1
-4 -6 -3 -1
-2 -3 -2 0
-2 -3 -1 -2
1
Generator of the Alexander module
(1+t,t,0,2t)
the Blanchfield form on it
2
63
First homology
of the double branched cover of 12n_0267
Z/63
-2 2
12n_0268
2

detected by
the Nakanishi index
-2+5t-2t^2
Seifert matrix of 12n_0268
0 -2
-1 -3
2
9
First homology
of the double branched cover of 12n_0268
Z/3+Z/3
0 0
12n_0269
2

detected by
the Nakanishi index
-1+9t-28t^2+41t^3-28t^4+9t^5-t^6
Seifert matrix of 12n_0269
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 1 0 0
1 0 0 -1 -1 0
-1 0 0 1 -1 1
2
117
First homology
of the double branched cover of 12n_0269
Z/39+Z/3
0 0
12n_0270
2

detected by
the Nakanishi index
-3+16t-25t^2+16t^3-3t^4
Seifert matrix of 12n_0270
0 1 2 1
0 1 0 0
1 0 3 1
1 0 2 2
2
63
First homology
of the double branched cover of 12n_0270
Z/21+Z/3
2 2
12n_0271
1

detected by
an unknotting move
-1+5t-12t^2+17t^3-12t^4+5t^5-t^6
Seifert matrix of 12n_0271
0 0 0 0 1 1
0 -1 -1 -1 0 1
-1 0 0 0 1 1
-1 0 -1 -1 0 1
0 0 0 0 2 1
1 0 1 0 0 0
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
1
53
First homology
of the double branched cover of 12n_0271
Z/53
0 0
12n_0272
1

detected by
an unknotting move
1-7t+20t^2-27t^3+20t^4-7t^5+t^6
Seifert matrix of 12n_0272
0 0 0 -1 0 -1
0 1 0 0 0 0
-1 0 0 -1 0 -1
-1 0 -1 0 0 0
0 0 -1 -1 -1 0
0 -1 0 1 0 2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-1-3+2t
83
First homology
of the double branched cover of 12n_0272
Z/83
2 2
12n_0273
2

detected by
the signature
-1+3t-3t^3+3t^5-t^6
Seifert matrix of 12n_0273
0 0 -1 0 -1 0
-1 -1 0 0 -1 0
0 0 0 0 1 0
-1 -1 0 -1 -1 0
-1 0 1 0 0 0
0 -1 0 -1 -1 -1
2
5
First homology
of the double branched cover of 12n_0273
Z/5
-4 4
12n_0274
2

detected by
the Lickorish test
-3+14t-21t^2+14t^3-3t^4
Seifert matrix of 12n_0274
-1 -3 -2 -1
-2 -3 -4 -2
-2 -4 -5 -2
-1 -3 -3 -2
2
55
First homology
of the double branched cover of 12n_0274
Z/55
-2 2
12n_0275
1

detected by
an unknotting move
2-9t+15t^2-9t^3+2t^4
Seifert matrix of 12n_0275
3 -1 2 0
0 1 -1 0
2 -1 1 0
1 0 1 -1
1
Generator of the Alexander module
(0,1,0,2-t)
the Blanchfield form on it
1
37
First homology
of the double branched cover of 12n_0275
Z/37
0 0
12n_0276
3

detected by
the Stoimenow criterion
1+t-7t^2+11t^3-7t^4+t^5+t^6
Seifert matrix of 12n_0276
1 0 0 0 0 0
0 1 0 0 0 0
1 0 1 0 0 0
1 0 0 1 0 0
1 1 -1 0 1 -1
1 0 1 0 0 1
2
25
First homology
of the double branched cover of 12n_0276
Z/5+Z/5
4 4
12n_0277
1

detected by
an unknotting move
2-8t+15t^2-17t^3+15t^4-8t^5+2t^6
Seifert matrix of 12n_0277
-1 -1 -1 0 -1 0
0 2 0 0 0 0
0 1 -1 0 0 0
-1 -1 -1 -1 -1 0
0 -1 -1 0 -1 0
0 1 0 0 0 1
1
Generator of the Alexander module
(-8-36t+10t^2+2t^3,3+2t+4t^2,-1-19t+15t^2+t^3-3t^4,-3+t-26t^2+31t^3+3t^4-19t^5+3t^6+9t^7,5t+7t^2+t^3-6t^4,3-3t-3t^2)
the Blanchfield form on it
x
67
First homology
of the double branched cover of 12n_0277
Z/67
-2 2
12n_0278
2

detected by
the Lickorish test
4-16t+25t^2-16t^3+4t^4
Seifert matrix of 12n_0278
-2 1 1 0
0 2 0 0
0 1 -1 0
0 1 0 1
1 or 2
65
First homology
of the double branched cover of 12n_0278
Z/65
0 0
12n_0279
1

detected by
an unknotting move
1-6t+11t^2-6t^3+t^4
Seifert matrix of 12n_0279
-15 -12 -10 -8
-11 -9 -7 -6
-10 -8 -6 -5
-5 -4 -3 -2
1
Generator of the Alexander module
(0,1,0,-1)
the Blanchfield form on it
9t^-1-18+9t
25
First homology
of the double branched cover of 12n_0279
Z/25
0 0
12n_0280
1

detected by
an unknotting move
1-6t+12t^2-13t^3+12t^4-6t^5+t^6
Seifert matrix of 12n_0280
-1 0 -1 -1 1 0
1 -2 1 1 -2 0
0 0 -1 -1 0 0
0 0 0 1 0 0
1 -1 1 1 -1 0
-1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,2-t)
the Blanchfield form on it
t^-2-6t^-1+11-6t+t^2
51
First homology
of the double branched cover of 12n_0280
Z/51
-2 2
12n_0281
1

detected by
an unknotting move
-1+6t-18t^2+27t^3-18t^4+6t^5-t^6
Seifert matrix of 12n_0281
-1 0 -1 -1 1 0
1 -2 1 1 -2 0
0 0 -1 -1 0 0
0 0 0 1 0 0
1 -1 1 1 -1 0
-1 0 -1 0 0 1
1
Generator of the Alexander module
(0,1+t,0,1,-1+t,-t)
the Blanchfield form on it
1
77
First homology
of the double branched cover of 12n_0281
Z/77
0 0
12n_0282
1

detected by
an unknotting move
1-5t+9t^2-5t^3+t^4
Seifert matrix of 12n_0282
0 0 -1 1
1 -1 0 -1
0 -1 -1 1
0 0 0 1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
t^-1-2+t
21
First homology
of the double branched cover of 12n_0282
Z/21
0 0
12n_0283
2

detected by
the Lickorish test
-1+6t-14t^2+16t^3-13t^4+16t^5-14t^6+6t^7-t^8
Seifert matrix of 12n_0283
-1 0 -1 -1 -1 0 0 -1
0 1 0 0 0 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 1 -1 -1 -1 1 0 -1
0 1 0 0 0 1 0 0
0 0 -1 0 0 0 -1 -1
0 0 -1 -1 0 1 0 -1
1
Generator of the Alexander module
(2t^2+3t^3-15t^4+13t^5+2t^6-9t^7+5t^8-t^9,0,2+7t-8t^2-5t^3+3t^4+3t^5+4t^6-9t^7+5t^8-t^9,-t+t^2+13t^3-20t^4+8t^5+4t^6-4t^7+t^8,-2t-3t^2+15t^3-13t^4-2t^5+9t^6-5t^7+t^8,0,1+3t-7t^2-6t^3+18t^4-t^5-12t^6+t^7+8t^8-5t^9+t^10,1+3t-6t^2+2t^3-7t^4+8t^5+3t^6-9t^7+5t^8-t^9)
the Blanchfield form on it
x
87
First homology
of the double branched cover of 12n_0283
Z/87
-2 2
12n_0284
1

detected by
an unknotting move
-1+5t-13t^2+19t^3-13t^4+5t^5-t^6
Seifert matrix of 12n_0284
1 0 0 0 0 0
-1 -2 -1 0 -1 -1
0 0 -1 0 0 -1
0 -1 -1 -1 0 0
-1 0 0 1 0 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,-1,1,0)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
57
First homology
of the double branched cover of 12n_0284
Z/57
0 0
12n_0285
1

detected by
an unknotting move
1-5t+9t^2-9t^3+9t^4-5t^5+t^6
Seifert matrix of 12n_0285
1 0 0 0 0 0
-1 -2 -1 0 -1 -1
0 0 -1 0 0 -1
0 -1 -1 -1 0 0
-1 0 0 1 0 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,-1,0)
the Blanchfield form on it
t^-2-6t^-1+11-6t+t^2
39
First homology
of the double branched cover of 12n_0285
Z/39
-2 2
12n_0286
1

detected by
an unknotting move
2-11t+19t^2-11t^3+2t^4
Seifert matrix of 12n_0286
1 0 0 0
-1 -1 0 1
1 1 -3 -2
1 1 -2 -1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
45
First homology
of the double branched cover of 12n_0286
Z/45
0 0
12n_0287
1

detected by
an unknotting move
-1+6t-15t^2+22t^3-23t^4+22t^5-15t^6+6t^7-t^8
Seifert matrix of 12n_0287
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 -1 0 0
0 0 1 0 0 0 0 0
0 0 1 1 0 0 -1 1
-1 0 -1 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
0 0 1 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,-t-8t^2+23t^3-35t^4+40t^5-39t^6+27t^7-11t^8+2t^9,0,-t-8t^2+23t^3-35t^4+40t^5-39t^6+27t^7-11t^8+2t^9,1-t+7t^2-31t^3+58t^4-75t^5+79t^6-66t^7+38t^8-13t^9+2t^10,0,0)
the Blanchfield form on it
x
111
First homology
of the double branched cover of 12n_0287
Z/111
2 2
12n_0288
1

detected by
an unknotting move
4-12t+17t^2-12t^3+4t^4
Seifert matrix of 12n_0288
-1 0 1 0
0 1 2 -1
0 2 0 -1
0 0 0 1
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
t^-1-1+t
49
First homology
of the double branched cover of 12n_0288
Z/49
0 0
12n_0289
3

detected by
the signature
4-12t+19t^2-21t^3+19t^4-12t^5+4t^6
Seifert matrix of 12n_0289
-1 0 -1 0 0 0
0 -1 0 0 0 0
0 0 -2 0 0 0
0 -1 -1 -1 0 1
0 0 0 0 -1 -1
0 1 1 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
91
First homology
of the double branched cover of 12n_0289
Z/91
-6 6
12n_0290
2

detected by
the signature
-1+7t-16t^2+21t^3-16t^4+7t^5-t^6
Seifert matrix of 12n_0290
-1 0 1 0 0 0
0 0 1 0 0 0
0 -1 -3 -2 -1 -1
0 -2 0 -2 -1 -1
0 0 0 0 -1 0
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(-t,0,0,2,0,1)
the Blanchfield form on it
2t^-1-3+2t
69
First homology
of the double branched cover of 12n_0290
Z/69
-4 4
12n_0291
1

detected by
an unknotting move
3-11t+22t^2-27t^3+22t^4-11t^5+3t^6
Seifert matrix of 12n_0291
-1 -2 0 -1 0 -1
0 -6 0 -3 0 -3
0 1 1 1 0 1
0 -3 0 -1 0 -1
0 1 1 1 1 1
0 -4 0 -2 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-3t^-2+9t^-1-13+9t-3t^2
99
First homology
of the double branched cover of 12n_0291
Z/99
2 2
12n_0292
4

detected by
the signature
2-4t+2t^2+4t^3-7t^4+4t^5+2t^6-4t^7+2t^8
Seifert matrix of 12n_0292
-1 0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 -1 -1 0 -1
0 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(1-2t,0,0,-1,0,0,0,0)
the Blanchfield form on it
2t^-3-t^-2-t^-1+3-t-t^2+2t^3
1
First homology
of the double branched cover of 12n_0292
0
-8 8
12n_0293
1

detected by
an unknotting move
2-3t+2t^2
Seifert matrix of 12n_0293
-8 2
3 -1
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
-t^-1+2-t
7
First homology
of the double branched cover of 12n_0293
Z/7
-2 2
12n_0294
2

detected by
the signature
1-5t+8t^2-6t^3+5t^4-6t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0294
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 0 0 -1
0 0 -1 -1 0 0 -1 0
0 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 0 -1 -1
0 0 0 0 0 1 0 0
0 0 0 -1 0 0 -1 0
-1 0 -1 -1 0 -1 -1 -1
2
45
First homology
of the double branched cover of 12n_0294
Z/45
-4 4
12n_0295
1

detected by
an unknotting move
1-9t+26t^2-35t^3+26t^4-9t^5+t^6
Seifert matrix of 12n_0295
0 2 0 -1 -1 2
1 1 0 1 0 0
0 0 -1 0 0 0
0 0 0 1 0 0
0 1 0 -1 0 1
1 1 -1 1 0 1
1 or 2
107
First homology
of the double branched cover of 12n_0295
Z/107
2 2
12n_0296
2

detected by
the signature
1-5t+8t^2-4t^3+t^4-4t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0296
-1 -1 0 -1 -1 -1 0 0
0 -1 0 -1 0 -1 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 0 -1 -1 -1 0 0
0 0 1 -1 0 -1 0 0
0 -1 0 0 -1 -1 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(-3+3t-4t^2+3t^3-t^4,0,-3-t^2+2t^3-t^4,0,0,0,1-3t+6t^2-4t^3+4t^4-2t^6+t^7,-t+3t^2-6t^3+4t^4-4t^5+2t^7-t^8)
the Blanchfield form on it
x
37
First homology
of the double branched cover of 12n_0296
Z/37
-4 4
12n_0297
2

detected by
the Lickorish test
2-11t+22t^2-25t^3+22t^4-11t^5+2t^6
Seifert matrix of 12n_0297
-1 1 -1 -1 0 0
0 -2 1 1 0 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 1 -1 0 -1 -1
0 0 0 0 0 1
2
95
First homology
of the double branched cover of 12n_0297
Z/95
-2 2
12n_0298
1

detected by
an unknotting move
-1+7t-21t^2+31t^3-21t^4+7t^5-t^6
Seifert matrix of 12n_0298
1 0 0 0 0 0
-1 -2 0 -1 0 -1
0 -1 -1 -1 0 0
0 0 0 1 0 0
0 -1 0 -1 -1 0
-1 0 1 0 0 0
1
Generator of the Alexander module
(0,2,-2t,3,0,2+2t)
the Blanchfield form on it
t^-2-4t^-1+7-4t+t^2
89
First homology
of the double branched cover of 12n_0298
Z/89
0 0
12n_0299
2

detected by
the signature
-3+12t-18t^2+19t^3-18t^4+12t^5-3t^6
Seifert matrix of 12n_0299
1 0 0 0 0 0
-1 -1 -1 0 -1 0
-1 0 -1 1 -1 1
0 0 0 -2 0 -1
-1 0 0 0 -1 1
0 0 0 -1 0 -2
1
Generator of the Alexander module
(0,-t-t^3+t^4,0,0,1-t^3,0)
the Blanchfield form on it
9t^-2-9t^-1+6-9t+9t^2
85
First homology
of the double branched cover of 12n_0299
Z/85
-4 4
12n_0300
1

detected by
an unknotting move
-1+7t-18t^2+25t^3-18t^4+7t^5-t^6
Seifert matrix of 12n_0300
0 0 2 -1 1 0
0 -1 0 0 -1 -1
1 0 1 1 1 1
0 0 0 1 0 0
1 0 1 0 0 0
1 0 2 -1 1 1
1
Generator of the Alexander module
(0,4-3t,-1+t,1-t,t-t^3,-1+3t-2t^2)
the Blanchfield form on it
-t^-1+4-t
77
First homology
of the double branched cover of 12n_0300
Z/77
0 0
12n_0301
1

detected by
an unknotting move
-1+5t-10t^2+12t^3-11t^4+12t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0301
-1 0 -1 -1 0 -1 0 0
0 1 0 0 0 -1 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 1 0 0 1 -1 0 0
0 0 -1 -1 0 -1 0 0
0 0 -1 0 0 -1 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-11t^-1+15-11t+5t^2-t^3
67
First homology
of the double branched cover of 12n_0301
Z/67
-2 2
12n_0302
1

detected by
an unknotting move
1-9t+27t^2-37t^3+27t^4-9t^5+t^6
Seifert matrix of 12n_0302
1 0 0 0 0 0
-1 -1 0 1 1 1
0 0 -2 1 0 1
1 0 0 -1 -1 -2
1 0 -1 -1 -2 -1
1 0 0 -1 -1 -1
1
Generator of the Alexander module
(-2-2t,2t^3,-t,1+t,-t,-2t-2t^2)
the Blanchfield form on it
2683t^-2-10971t^-1+15761-10971t+2683t^2
111
First homology
of the double branched cover of 12n_0302
Z/111
-2 2
12n_0303
2

detected by
the signature
-1+5t-9t^2+11t^3-9t^4+5t^5-t^6
Seifert matrix of 12n_0303
-1 0 0 0 -1 0
0 0 0 0 -1 0
0 0 -1 -1 0 -1
0 0 0 -1 0 -1
0 -1 0 0 -3 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
41
First homology
of the double branched cover of 12n_0303
Z/41
-4 4
12n_0304
1

detected by
an unknotting move
3-9t+15t^2-17t^3+15t^4-9t^5+3t^6
Seifert matrix of 12n_0304
-1 0 1 0 0 0
0 4 1 0 2 0
0 2 -1 0 1 0
0 2 1 1 1 1
0 1 0 0 1 0
0 2 1 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-2-3t^-1+3-3t+2t^2
71
First homology
of the double branched cover of 12n_0304
Z/71
2 2
12n_0305
4

detected by
the signature
2-4t+4t^2-3t^3+3t^4-3t^5+4t^6-4t^7+2t^8
Seifert matrix of 12n_0305
-1 0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 0 0 -1 0 -1 0 -1
0 -1 -1 0 -1 0 0 0
0 -1 0 0 -1 -1 0 0
0 0 0 -1 0 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(-1+2t,0,0,0,1,0,0,0)
the Blanchfield form on it
2t^-3-t^-2+t^-1-1+t-t^2+2t^3
29
First homology
of the double branched cover of 12n_0305
Z/29
-8 8
12n_0306
1

detected by
an unknotting move
-2+9t-13t^2+9t^3-2t^4
Seifert matrix of 12n_0306
-1 0 -1 0
0 0 -1 0
0 -2 -6 -2
0 -1 -3 -2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
1
35
First homology
of the double branched cover of 12n_0306
Z/35
-2 2
12n_0307
1

detected by
an unknotting move
6-19t+27t^2-19t^3+6t^4
Seifert matrix of 12n_0307
-1 0 1 0
0 2 1 0
0 1 -1 0
0 1 1 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
3t^-2-10t^-1+14-10t+3t^2
77
First homology
of the double branched cover of 12n_0307
Z/77
0 2
12n_0308
3

detected by
the signature
4-10t+12t^2-11t^3+12t^4-10t^5+4t^6
Seifert matrix of 12n_0308
-1 0 -1 0 0 0
0 -1 -1 0 0 0
0 0 -2 0 0 0
0 0 0 -2 0 1
0 -1 -1 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-3+6t^-2-8t^-1+8-8t+6t^2-2t^3
63
First homology
of the double branched cover of 12n_0308
Z/63
-6 6
12n_0309
1

detected by
an unknotting move
1-t-t^2+3t^3-t^4-t^5+t^6
Seifert matrix of 12n_0309
-1 0 1 0 0 0
0 0 1 0 1 0
0 1 -1 0 1 0
0 1 1 1 1 1
0 0 0 0 1 0
0 1 1 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
t^-1-1+t
1
First homology
of the double branched cover of 12n_0309
0
0 0
12n_0310
1

detected by
an unknotting move
2-5t+7t^2-5t^3+2t^4
Seifert matrix of 12n_0310
-1 0 1 0
0 0 1 0
0 1 -1 0
0 1 1 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
21
First homology
of the double branched cover of 12n_0310
Z/21
0 2
12n_0311
1

detected by
an unknotting move
-3+13t-19t^2+13t^3-3t^4
Seifert matrix of 12n_0311
1 1 0 0
0 1 0 0
-1 0 1 -1
-1 1 -1 -2
1
Generator of the Alexander module
(0,0,-2+t,-1)
the Blanchfield form on it
t^-1-2+t
51
First homology
of the double branched cover of 12n_0311
Z/51
2 2
12n_0312
1

detected by
an unknotting move
-1+5t-11t^2+15t^3-11t^4+5t^5-t^6
Seifert matrix of 12n_0312
-1 0 0 0 0 -1
0 -2 0 1 0 -1
0 -1 0 0 0 -1
0 0 0 1 0 0
0 -1 -1 0 0 -1
0 -1 -1 1 -1 -2
1
Generator of the Alexander module
(-3+4t-t^2,0,0,0,2-t,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
49
First homology
of the double branched cover of 12n_0312
Z/49
0 0
12n_0314
1

detected by
an unknotting move
1-6t+13t^2-15t^3+13t^4-6t^5+t^6
Seifert matrix of 12n_0314
1 0 0 0 0 0
-1 -2 0 -1 -1 -1
0 -1 -1 -1 0 0
0 0 0 1 0 0
-1 0 1 0 0 0
0 0 0 1 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
t^-1-2+t
55
First homology
of the double branched cover of 12n_0314
Z/55
2 2
12n_0315
1

detected by
an unknotting move
-1+6t-14t^2+19t^3-14t^4+6t^5-t^6
Seifert matrix of 12n_0315
0 0 0 0 1 -1
1 -1 -1 0 1 0
1 0 -1 0 1 0
1 1 1 1 1 0
0 0 0 0 1 0
-1 -1 0 0 0 0
1
Generator of the Alexander module
(0,0,1,0,0,-1)
the Blanchfield form on it
t^-1-1+t
61
First homology
of the double branched cover of 12n_0315
Z/61
0 0
12n_0316
2

detected by
the signature
-1+7t-15t^2+19t^3-15t^4+7t^5-t^6
Seifert matrix of 12n_0316
-4 -1 0 -3 -3 -2
-2 -1 0 -3 -2 -1
-1 0 -1 -1 -1 0
-4 -2 0 -5 -4 -2
-4 -1 0 -3 -4 -2
-1 0 0 -1 -1 -1
1 or 2
65
First homology
of the double branched cover of 12n_0316
Z/65
-4 4
12n_0317
2

detected by
the Lickorish test
-2+9t-19t^2+25t^3-19t^4+9t^5-2t^6
Seifert matrix of 12n_0317
-1 0 0 2 1 0
0 0 0 1 0 0
0 -1 1 1 1 0
0 2 -2 -6 -4 -2
0 0 -1 -2 -1 -1
0 -1 1 1 1 1
1
Generator of the Alexander module
(t,0,0,2,1,0)
the Blanchfield form on it
-2t^-2+6t^-1-7+6t-2t^2
85
First homology
of the double branched cover of 12n_0317
Z/85
0 0
12n_0318
1

detected by
an unknotting move
1-t-t^2+3t^3-t^4-t^5+t^6
Seifert matrix of 12n_0318
-1 0 1 0 0 1
0 1 1 1 1 1
0 0 0 0 1 -1
0 2 1 2 1 1
0 0 0 0 1 0
0 1 0 0 1 0
1
Generator of the Alexander module
(-1-t,0,0,0,0,-1)
the Blanchfield form on it
3t^-2+t^-1-5+t+3t^2
1
First homology
of the double branched cover of 12n_0318
0
0 0
12n_0319
2

detected by
the signature
-2+6t-8t^2+9t^3-8t^4+6t^5-2t^6
Seifert matrix of 12n_0319
-1 -1 1 -1 0 1
0 -4 0 -2 0 -2
0 -1 -1 0 0 -1
0 -1 0 0 0 -1
-1 -1 1 -1 -1 1
0 -1 -1 0 0 -2
1
Generator of the Alexander module
(0,2-10t-2t^2+5t^3-3t^4,1+t,1-4t-t^2+2t^3-t^4,-1-t+4t^2-2t^4+t^5,2+6t-2t^3+2t^4)
the Blanchfield form on it
41t^-4+172t^-3-990t^-2+1904t^-1-2328+1904t-990t^2+172t^3+41t^4
41
First homology
of the double branched cover of 12n_0319
Z/41
-4 4
12n_0320
1

detected by
an unknotting move
-2+11t-25t^2+33t^3-25t^4+11t^5-2t^6
Seifert matrix of 12n_0320
-1 0 1 0 0 1
0 2 1 1 1 1
0 0 -1 0 1 -1
0 2 1 2 1 1
0 0 0 0 1 0
0 1 0 0 1 -1
1
Generator of the Alexander module
(-t,1,0,0,0,t)
the Blanchfield form on it
2t^-2-5t^-1+8-5t+2t^2
109
First homology
of the double branched cover of 12n_0320
Z/109
0 0
12n_0321
1

detected by
an unknotting move
3-5t+3t^2
Seifert matrix of 12n_0321
-23 4
5 -1
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
-t^-1+2-t
11
First homology
of the double branched cover of 12n_0321
Z/11
-2 2
12n_0322
1

detected by
an unknotting move
-2+6t-7t^2+6t^3-2t^4
Seifert matrix of 12n_0322
-1 0 0 -1
1 -1 -2 -1
2 -2 -3 -1
2 -2 -4 -4
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-1+1-t
23
First homology
of the double branched cover of 12n_0322
Z/23
-2 2
12n_0323
1

detected by
an unknotting move
4-13t+19t^2-13t^3+4t^4
Seifert matrix of 12n_0323
-13 -12 -7 -10
-16 -16 -8 -12
-6 -5 -3 -4
-12 -11 -6 -8
1 or 2
53
First homology
of the double branched cover of 12n_0323
Z/53
0 0
12n_0324
1

detected by
an unknotting move
-5+17t-23t^2+17t^3-5t^4
Seifert matrix of 12n_0324
-3 -7 -6 -5
-10 -30 -25 -20
-8 -23 -19 -16
-6 -17 -15 -11
1 or 2
67
First homology
of the double branched cover of 12n_0324
Z/67
-2 2
12n_0325
1

detected by
an unknotting move
-2+11t-26t^2+35t^3-26t^4+11t^5-2t^6
Seifert matrix of 12n_0325
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 -1 -2 -1 -2 0
0 1 0 1 0 0
0 0 -1 -1 -2 0
0 1 1 1 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
113
First homology
of the double branched cover of 12n_0325
Z/113
0 0
12n_0326
2

detected by
the signature
-1+4t-8t^2+9t^3-9t^4+9t^5-8t^6+4t^7-t^8
Seifert matrix of 12n_0326
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 1 1 0 0 0
0 0 0 0 1 0 0 0
0 0 -1 -1 0 -1 0 0
-1 -1 0 -1 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,-2t,0,1)
the Blanchfield form on it
-3t^-3+19t^-2-51t^-1+63-51t+19t^2-3t^3
53
First homology
of the double branched cover of 12n_0326
Z/53
-4 4
12n_0327
2

detected by
the signature
-1+4t-9t^2+11t^3-11t^4+11t^5-9t^6+4t^7-t^8
Seifert matrix of 12n_0327
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 1 0 0
0 0 0 1 1 0 0 0
0 0 0 0 1 0 0 0
0 0 0 -1 0 1 0 0
-1 -1 0 -1 -1 0 1 1
0 0 0 0 0 0 0 1
1 or 2
61
First homology
of the double branched cover of 12n_0327
Z/61
4 4
12n_0328
3

detected by
the signature
-1+3t^2-5t^3+5t^4-5t^5+3t^6-t^8
Seifert matrix of 12n_0328
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 -1 -1 0 0 0
0 0 -1 -1 0 -1 0 0
-1 -1 0 -1 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,-1,0,0,0,0,0,1-t)
the Blanchfield form on it
-t^-3+4t^-1-7+4t-t^3
19
First homology
of the double branched cover of 12n_0328
Z/19
-6 6
12n_0329
2

detected by
the signature
1+t-6t^2+9t^3-6t^4+t^5+t^6
Seifert matrix of 12n_0329
1 0 0 0 0 0
0 1 0 0 0 0
1 0 1 0 -1 0
0 0 0 1 1 0
1 1 0 0 1 0
0 0 0 1 1 1
1 or 2
21
First homology
of the double branched cover of 12n_0329
Z/21
4 4
12n_0330
1

detected by
an unknotting move
2-9t+20t^2-25t^3+20t^4-9t^5+2t^6
Seifert matrix of 12n_0330
1 0 0 0 0 0
0 -1 0 0 -1 0
1 0 1 0 -1 0
0 0 0 -1 0 -1
1 0 0 -1 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,-2t^2,-1-2t,1,0,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
87
First homology
of the double branched cover of 12n_0330
Z/87
-2 2
12n_0331
2

detected by
the signature
-2+7t-9t^2+9t^3-9t^4+7t^5-2t^6
Seifert matrix of 12n_0331
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 0 -1 0
0 0 0 1 1 0
1 1 0 0 1 0
0 0 0 1 1 1
1
Generator of the Alexander module
(1-16t^2+8t^3,0,1-16t^2+8t^3,-16t^2,2+t-8t^2+8t^4,-2-3t+31t^2+8t^3-8t^4-8t^5)
the Blanchfield form on it
3907t^-2-13158t^-1+16307-13158t+3907t^2
45
First homology
of the double branched cover of 12n_0331
Z/45
4 4
12n_0332
2

detected by
the Nakanishi index
2-2t+t^2-2t^3+2t^4
Seifert matrix of 12n_0332
1 0 0 0
0 1 0 0
1 0 1 1
-1 -1 0 2
2
9
First homology
of the double branched cover of 12n_0332
Z/3+Z/3
4 4
12n_0333
2

detected by
the Nakanishi index
3-11t+17t^2-11t^3+3t^4
Seifert matrix of 12n_0333
1 0 0 0
0 -1 0 1
1 0 1 1
-1 0 0 -3
2
45
First homology
of the double branched cover of 12n_0333
Z/15+Z/3
0 0
12n_0334
2

detected by
the Nakanishi index
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 12n_0334
1 0 0 0
0 1 0 0
1 0 -2 1
-1 -1 0 2
2
63
First homology
of the double branched cover of 12n_0334
Z/21+Z/3
2 2
12n_0335
2

detected by
the Lickorish test
2-10t+22t^2-27t^3+22t^4-10t^5+2t^6
Seifert matrix of 12n_0335
-2 1 0 0 -1 0
0 1 0 0 0 0
-1 1 1 0 -1 0
-1 0 0 -1 0 0
0 0 0 0 -1 0
-1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,t,0,t^2)
the Blanchfield form on it
2
95
First homology
of the double branched cover of 12n_0335
Z/95
-2 2
12n_0336
2

detected by
the signature
-1+2t-t^3+2t^5-t^6
Seifert matrix of 12n_0336
-5 -1 -1 -2 -2 -1
-2 0 -1 -1 -1 -1
0 0 1 0 0 0
-1 0 0 0 0 0
-2 0 0 -1 0 0
-2 0 -1 -1 -1 0
1
Generator of the Alexander module
(2,1,0,0,1-t,1)
the Blanchfield form on it
t^-2+t^2
5
First homology
of the double branched cover of 12n_0336
Z/5
4 4
12n_0337
1

detected by
an unknotting move
1-9t+25t^2-33t^3+25t^4-9t^5+t^6
Seifert matrix of 12n_0337
-1 0 -1 0 0 1
0 -1 0 0 0 0
0 0 1 0 0 0
-1 0 0 1 1 0
0 0 0 0 1 0
0 -1 1 0 0 1
1
Generator of the Alexander module
(0,2-t,-2+t,1-2t^2+t^3,1+2t-t^2,2t-t^2)
the Blanchfield form on it
-t^-2+8t^-1-16+8t-t^2
103
First homology
of the double branched cover of 12n_0337
Z/103
2 2
12n_0338
4

detected by
the signature
2-4t+4t^2-2t^3+t^4-2t^5+4t^6-4t^7+2t^8
Seifert matrix of 12n_0338
-1 0 0 0 0 0 0 0
0 -1 0 -1 0 0 -1 1
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 0 0 0 1
0 0 0 0 -1 0 0 -1
0 -1 0 -1 0 -1 -1 1
0 0 0 -1 0 0 -1 1
1 0 1 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-t^-2+t^-1-1+t-t^2+t^3
25
First homology
of the double branched cover of 12n_0338
Z/25
-8 8
12n_0339
2

detected by
the Lickorish test
3-11t+21t^2-25t^3+21t^4-11t^5+3t^6
Seifert matrix of 12n_0339
1 0 0 -1 1 0
1 -1 0 1 0 0
0 0 -1 0 0 0
-1 0 -1 -2 0 0
0 0 0 0 1 0
1 -1 0 1 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
3t^-2-9t^-1+13-9t+3t^2
95
First homology
of the double branched cover of 12n_0339
Z/95
-2 2
12n_0340
1

detected by
an unknotting move
-1+3t-3t^2+3t^3-3t^4+3t^5-t^6
Seifert matrix of 12n_0340
-3 -2 -2 -2 0 -2
-2 -1 -2 -2 0 -1
-3 -2 -3 -2 0 -2
-2 -1 -2 -1 0 -1
-1 -1 -1 -1 -1 -1
-2 -2 -2 -2 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
1
17
First homology
of the double branched cover of 12n_0340
Z/17
0 2
12n_0341
3

detected by
the signature
4-10t+13t^2-13t^3+13t^4-10t^5+4t^6
Seifert matrix of 12n_0341
-1 0 0 0 0 0
0 -2 0 1 0 -1
-1 0 -1 0 0 0
-1 0 -1 -1 0 1
0 0 0 0 -1 -1
1 0 1 0 0 -2
1 or 2
67
First homology
of the double branched cover of 12n_0341
Z/67
-6 6
12n_0342
1

detected by
an unknotting move
4-13t+19t^2-13t^3+4t^4
Seifert matrix of 12n_0342
5 6 2 -2
5 5 2 -2
2 2 0 -1
0 0 0 1
1
Generator of the Alexander module
(-6t+4t^2+11t^3-20t^4+14t^5-4t^6,-6t+4t^2+11t^3-20t^4+14t^5-4t^6,1-10t+2t^2+27t^3-42t^4+28t^5-8t^6,0)
the Blanchfield form on it
4t^-1-1+4t
53
First homology
of the double branched cover of 12n_0342
Z/53
0 0
12n_0343
1

detected by
an unknotting move
-4+15t-21t^2+15t^3-4t^4
Seifert matrix of 12n_0343
-5 -4 -4 -2
-4 -2 -4 -2
-5 -4 -5 -2
-1 -1 -1 -1
1
Generator of the Alexander module
(-35+38t-38t^2,34-34t+34t^2,-31+26t-26t^2,-42+38t-38t^2)
the Blanchfield form on it
10065t^-3-67579t^-2+162292t^-1-214238+162292t-67579t^2+10065t^3
59
First homology
of the double branched cover of 12n_0343
Z/59
-2 2
12n_0344
2

detected by
the signature
1-4t+10t^2-15t^3+17t^4-15t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0344
-1 0 -1 -1 0 0 -1 0
0 1 0 0 1 0 0 0
0 0 0 -1 0 1 -1 1
0 1 -1 0 1 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 1
0 0 0 -1 0 1 0 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
2t^-3-5t^-2+8t^-1-9+8t-5t^2+2t^3
77
First homology
of the double branched cover of 12n_0344
Z/77
4 4
12n_0345
1

detected by
an unknotting move
-1+4t-8t^2+13t^3-15t^4+13t^5-8t^6+4t^7-t^8
Seifert matrix of 12n_0345
-1 0 -1 -1 0 0 -1 0
0 1 0 0 1 0 0 0
0 0 -2 -1 0 0 -2 0
0 1 -1 0 1 0 -1 0
0 0 0 0 1 0 0 0
0 0 -1 0 0 -1 -1 0
0 0 -1 -1 0 0 -2 0
0 0 -1 0 0 -1 -1 -1
1
Generator of the Alexander module
(-t,0,1,1,0,-t,1,-1)
the Blanchfield form on it
t^-2-2t^-1+3-2t+t^2
67
First homology
of the double branched cover of 12n_0345
Z/67
-2 2
12n_0346
1

detected by
an unknotting move
1-2t+2t^2-t^3+t^4-t^5+2t^6-2t^7+t^8
Seifert matrix of 12n_0346
-1 0 -1 -1 0 0 -1 0
0 -1 0 -1 0 0 0 0
0 0 0 -1 0 1 -1 1
0 0 -1 -2 0 0 -1 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 0 1 0 1
0 0 0 -1 0 1 0 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,1,0,0,0)
the Blanchfield form on it
2t^-3-3t^-2+t^-1+2+t-3t^2+2t^3
13
First homology
of the double branched cover of 12n_0346
Z/13
0 2
12n_0347
1

detected by
an unknotting move
1-3t+7t^2-9t^3+7t^4-3t^5+t^6
Seifert matrix of 12n_0347
-1 0 -1 0 1 0
0 1 0 1 0 0
0 1 0 1 1 0
0 0 0 1 0 0
0 0 1 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1+t,0,0,0,-t^2,0)
the Blanchfield form on it
t^-1-2+t
31
First homology
of the double branched cover of 12n_0347
Z/31
2 2
12n_0348
1

detected by
an unknotting move
1-7t+19t^2-25t^3+19t^4-7t^5+t^6
Seifert matrix of 12n_0348
0 -1 0 0 -1 -1
-1 0 0 0 0 -1
-1 -1 -1 0 -1 -1
-1 -1 0 1 -1 -1
-1 -1 0 0 0 -1
-2 -1 -1 0 -1 -1
1
Generator of the Alexander module
(0,1-2t,-2,-1,2t,-2)
the Blanchfield form on it
-19t^-2+126t^-1-200+126t-19t^2
79
First homology
of the double branched cover of 12n_0348
Z/79
2 2
12n_0349
2

detected by
the signature
-1+4t-2t^2-t^3-2t^4+4t^5-t^6
Seifert matrix of 12n_0349
1 0 1 0 0 0
0 1 1 0 1 0
0 0 1 0 0 0
-1 -1 0 1 -1 -1
0 0 1 0 1 0
-1 0 0 0 0 -1
1
Generator of the Alexander module
(0,1,0,2,0,1)
the Blanchfield form on it
-t^-2-14t^-1+26-14t-t^2
13
First homology
of the double branched cover of 12n_0349
Z/13
4 4
12n_0350
1

detected by
an unknotting move
1-8t+25t^2-35t^3+25t^4-8t^5+t^6
Seifert matrix of 12n_0350
2 1 1 0 1 1
1 2 1 0 2 1
0 0 1 0 0 0
-1 -1 0 -1 -1 -1
1 1 1 0 2 1
0 1 0 0 1 0
1
Generator of the Alexander module
(0,0,0,2-t,-1,1)
the Blanchfield form on it
-1
103
First homology
of the double branched cover of 12n_0350
Z/103
2 2
12n_0351
1

detected by
an unknotting move
1-5t+7t^2-5t^3+7t^4-5t^5+t^6
Seifert matrix of 12n_0351
1 0 -1 -2 -1 0
0 -1 0 2 1 -1
0 0 -1 0 0 0
0 0 -1 -2 -1 0
0 0 -1 -1 0 0
0 0 0 2 1 -1
1
Generator of the Alexander module
(-2,2,0,-1,0,1)
the Blanchfield form on it
-t^-1+2-t
31
First homology
of the double branched cover of 12n_0351
Z/31
-2 2
12n_0352
1

detected by
an unknotting move
1-3t+t^2+3t^3+t^4-3t^5+t^6
Seifert matrix of 12n_0352
0 0 0 0 -1 0
-1 -1 0 0 -1 -1
0 0 1 0 0 -1
-1 0 0 -1 -1 0
-2 -1 0 0 -1 -1
-1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,1,0,0,1,0)
the Blanchfield form on it
1
7
First homology
of the double branched cover of 12n_0352
Z/7
-2 2
12n_0353
1

detected by
an unknotting move
1-9t+25t^2-33t^3+25t^4-9t^5+t^6
Seifert matrix of 12n_0353
1 0 0 1 0 0
-1 0 0 0 -1 -1
0 0 -1 0 0 -1
0 0 0 1 0 0
-1 -1 0 1 0 -1
-1 0 0 0 -1 0
1
Generator of the Alexander module
(5t^2-3t^3+12t^4-23t^5-147t^6-9t^7-31t^8+74t^9-6t^10+72t^11,t+t^2+21t^3+6t^4+18t^5,2-4t-2t^2-31t^3-113t^4-21t^5+5t^6+74t^7-6t^8+72t^9,0,-6+11t+6t^2+76t^3+270t^4+18t^5-46t^6-148t^7+12t^8-144t^9,1+2t+5t^2-3t^3-6t^4-18t^5)
the Blanchfield form on it
x
103
First homology
of the double branched cover of 12n_0353
Z/103
2 2
12n_0354
1

detected by
an unknotting move
1-4t+5t^2-3t^3+5t^4-4t^5+t^6
Seifert matrix of 12n_0354
2 0 2 1 0 1
0 -1 1 1 1 0
1 0 2 1 0 1
1 0 2 2 0 1
1 0 2 1 1 1
0 0 1 1 0 0
1
Generator of the Alexander module
(0,t,1,1,3,-6)
the Blanchfield form on it
-26t^-2+111t^-1-97+111t-26t^2
23
First homology
of the double branched cover of 12n_0354
Z/23
2 2
12n_0355
2

detected by
A(F_2)
1-3t+2t^2+t^3+2t^4-3t^5+t^6
Seifert matrix of 12n_0355
1 0 0 0 0 0
0 1 1 0 1 -1
1 0 1 0 0 -1
0 0 0 -1 0 -1
1 0 0 -1 1 -1
0 0 0 0 0 -1
2
11
First homology
of the double branched cover of 12n_0355
Z/11
2 2
12n_0356
2

detected by
A(F_2)
-1+5t-14t^2+21t^3-14t^4+5t^5-t^6
Seifert matrix of 12n_0356
1 0 0 0 0 0
0 1 1 0 1 -1
1 0 1 0 0 -1
0 0 0 -1 0 -1
1 0 0 -1 -1 -1
0 0 0 0 0 -1
2
61
First homology
of the double branched cover of 12n_0356
Z/61
0 0
12n_0357
2

detected by
the Lickorish test
1-9t+24t^2-31t^3+24t^4-9t^5+t^6
Seifert matrix of 12n_0357
1 0 0 0 0 0
0 1 1 0 1 -1
1 0 -1 0 0 -1
0 0 0 -1 0 -1
1 0 0 -1 -1 -1
0 0 0 0 0 -1
2
99
First homology
of the double branched cover of 12n_0357
Z/99
-2 2
12n_0358
1

detected by
an unknotting move
-3+11t-15t^2+11t^3-3t^4
Seifert matrix of 12n_0358
1 0 0 0
1 1 2 3
1 2 3 4
0 2 2 5
1
Generator of the Alexander module
(0,1,1,0)
the Blanchfield form on it
t^-1-2+t
43
First homology
of the double branched cover of 12n_0358
Z/43
2 2
12n_0359
1

detected by
an unknotting move
3-17t+29t^2-17t^3+3t^4
Seifert matrix of 12n_0359
5 -9 6 2
-8 13 -8 -3
6 -9 5 3
2 -3 2 2
1
Generator of the Alexander module
(0,0,-1,1)
the Blanchfield form on it
-16t^-2+65t^-1-98+65t-16t^2
69
First homology
of the double branched cover of 12n_0359
Z/69
0 0
12n_0360
1

detected by
an unknotting move
3-12t+19t^2-12t^3+3t^4
Seifert matrix of 12n_0360
0 -1 -1 -1
-2 -3 -2 -2
-2 -3 -2 -3
-3 -3 -3 -4
1
Generator of the Alexander module
(0,-2+3t,-1+t,1-2t)
the Blanchfield form on it
-10t^-1+25-10t
49
First homology
of the double branched cover of 12n_0360
Z/49
0 0
12n_0361
2

detected by
the signature
-3+11t-15t^2+15t^3-15t^4+11t^5-3t^6
Seifert matrix of 12n_0361
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 -2 0 -1 -1
0 0 0 -1 0 -1
1 -1 -1 -1 -2 -1
0 0 0 0 0 -1
1 or 2
73
First homology
of the double branched cover of 12n_0361
Z/73
-4 4
12n_0362
1

detected by
an unknotting move
1-4t+7t^2-7t^3+7t^4-4t^5+t^6
Seifert matrix of 12n_0362
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 -2 0 -1 -1
0 0 0 1 0 0
1 -1 -1 -1 0 -1
0 0 0 1 0 1
1
Generator of the Alexander module
(0,t,1,0,1,-t)
the Blanchfield form on it
-1
31
First homology
of the double branched cover of 12n_0362
Z/31
2 2
12n_0363
1

detected by
an unknotting move
1-8t+21t^2-27t^3+21t^4-8t^5+t^6
Seifert matrix of 12n_0363
2 0 1 1 1 1
0 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
1 1 1 1 2 1
0 0 0 1 1 0
1
Generator of the Alexander module
(-5+10t-9t^2-7t^3+22t^4-13t^5+2t^6+8t^7-8t^8+2t^9,0,0,0,2t-5t^2+3t^4-5t^5+4t^6-t^7,-2+4t-7t^2+t^3+3t^4-5t^5+4t^6-t^7)
the Blanchfield form on it
x
87
First homology
of the double branched cover of 12n_0363
Z/87
2 2
12n_0364
2

detected by
the Lickorish test
2-11t+23t^2-27t^3+23t^4-11t^5+2t^6
Seifert matrix of 12n_0364
2 0 -1 0 0 0
1 -1 -1 0 0 0
0 0 -1 0 0 0
0 1 0 -1 0 1
1 0 -1 0 1 1
1 -1 -1 0 0 -1
1
Generator of the Alexander module
(49+47t-10t^2+40t^3-124t^4-136t^5-156t^6+702t^7-1200t^8+1532t^9-1016t^10+304t^11-32t^12,5-10t+8t^2-6t^3-66t^4+154t^5-194t^6+180t^7-88t^8+16t^9,7+127t+17t^2+140t^3+536t^4-1238t^5+622t^6+36t^7-1130t^8+1372t^9-448t^10-48t^11+32t^12,40-10t+64t^2+64t^3-388t^4+588t^5-684t^6+460t^7-144t^8+16t^9,-47-36t-31t
the Blanchfield form on it
x
99
First homology
of the double branched cover of 12n_0364
Z/99
-2 2
12n_0365
2

detected by
the Lickorish test
2-11t+23t^2-27t^3+23t^4-11t^5+2t^6
Seifert matrix of 12n_0365
1 0 0 0 0 0
-1 -1 -1 1 0 0
0 0 1 0 1 0
0 0 -1 0 -1 1
0 0 0 0 1 0
-1 0 -1 2 -1 1
1
Generator of the Alexander module
(0,28t+4t^2-134t^3+105t^4-26t^5,-29+107t-136t^2+15t^3+33t^4-13t^5,-57-11t+90t^2-59t^3+13t^4,-86+153t-149t^2+15t^3+33t^4-13t^5,-115t+146t^2-193t^3+118t^4-26t^5)
the Blanchfield form on it
12t^-2-34t^-1+35-34t+12t^2
99
First homology
of the double branched cover of 12n_0365
Z/99
2 2
12n_0366
2

detected by
the signature
1+2t-8t^2+11t^3-8t^4+2t^5+t^6
Seifert matrix of 12n_0366
1 0 0 0 0 0
0 1 1 0 1 0
1 0 1 0 0 -1
0 1 1 1 1 0
1 0 0 0 1 0
1 0 0 0 0 1
1 or 2
29
First homology
of the double branched cover of 12n_0366
Z/29
4 4
12n_0367
1

detected by
an unknotting move
-1+10t-30t^2+43t^3-30t^4+10t^5-t^6
Seifert matrix of 12n_0367
1 0 0 0 0 0
0 1 1 0 1 0
1 0 -1 0 0 -1
0 1 1 1 1 0
1 0 0 0 -1 -1
1 0 0 0 -1 -2
1
Generator of the Alexander module
(0,-t^2,1-t,0,0,0)
the Blanchfield form on it
t^-2-8t^-1+13-8t+t^2
125
First homology
of the double branched cover of 12n_0367
Z/125
0 0
12n_0368
3

detected by
the signature
-1+4t-5t^2+3t^3-t^4+3t^5-5t^6+4t^7-t^8
Seifert matrix of 12n_0368
-1 0 0 0 0 0 0 0
0 -1 0 -1 -1 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 0 0 -1 -1 -1 0 0
-1 0 -1 0 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1-t^2,0,0,0,-2t+t^3,2t^2-t^4)
the Blanchfield form on it
-2t^-3+5t^-2-t^-1+1-t+5t^2-2t^3
27
First homology
of the double branched cover of 12n_0368
Z/27
-6 6
12n_0369
1

detected by
an unknotting move
-1+4t-9t^2+15t^3-17t^4+15t^5-9t^6+4t^7-t^8
Seifert matrix of 12n_0369
-1 0 0 0 0 0 0 0
0 1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 -1 1 0 0
0 0 0 0 -1 0 0 0
0 1 0 0 -1 1 0 0
-1 0 -1 0 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,-2t^2-t^4,2t^2+t^4,0,1+2t+3t^3+t^5,0,0)
the Blanchfield form on it
-t^-1+2-t
75
First homology
of the double branched cover of 12n_0369
Z/75
-2 2
12n_0370
1

detected by
an unknotting move
-1+2t-t^3+2t^5-t^6
Seifert matrix of 12n_0370
-1 0 -1 1 0 0
0 1 0 0 0 0
0 0 0 0 0 -1
0 1 1 -1 0 1
0 0 0 -1 -1 0
0 1 0 1 0 0
1
Generator of the Alexander module
(t,0,-1,1,0,0)
the Blanchfield form on it
1
5
First homology
of the double branched cover of 12n_0370
Z/5
0 2
12n_0371
1

detected by
an unknotting move
1-2t+2t^2-t^3+2t^4-2t^5+t^6
Seifert matrix of 12n_0371
-1 0 -1 1 0 0
0 -1 0 -1 0 -1
0 0 -2 1 0 0
0 0 2 -1 1 -1
0 0 0 0 1 0
0 0 1 -1 0 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
1
11
First homology
of the double branched cover of 12n_0371
Z/11
-2 2
12n_0372
1

detected by
an unknotting move
1-4t+10t^2-13t^3+10t^4-4t^5+t^6
Seifert matrix of 12n_0372
-1 0 -1 1 0 0
0 -1 0 -1 0 -1
0 0 -2 1 0 0
0 0 2 -1 1 -1
0 0 0 0 1 0
0 0 1 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
1
43
First homology
of the double branched cover of 12n_0372
Z/43
-2 2
12n_0373
2

detected by
the signature
-1+8t-18t^2+23t^3-18t^4+8t^5-t^6
Seifert matrix of 12n_0373
-1 0 -1 1 0 0
0 -1 0 -1 0 -1
0 0 -2 1 0 0
0 0 2 -3 0 -1
0 0 0 -1 -1 0
0 0 1 -1 0 0
1 or 2
77
First homology
of the double branched cover of 12n_0373
Z/77
-4 4
12n_0374
3

detected by
the signature
-2+3t-6t^3+9t^4-6t^5+3t^7-2t^8
Seifert matrix of 12n_0374
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 -1
-1 -1 0 -1 0 0 0 0
0 0 0 -1 -1 1 0 0
0 0 0 1 0 -2 0 0
0 0 -1 0 0 -1 -1 -1
-1 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,-t^2,t,0,1+t^2,-t^2,0,0)
the Blanchfield form on it
-2t^-2+5t^-1-7+5t-2t^2
11
First homology
of the double branched cover of 12n_0374
Z/11
-6 6
12n_0375
2

detected by
the signature
-1+6t-13t^2+17t^3-13t^4+6t^5-t^6
Seifert matrix of 12n_0375
-3 -2 -4 0 -2 0
0 -1 0 0 0 0
-5 -2 -6 0 -3 0
-2 0 -2 -1 -1 0
-2 -1 -2 1 -2 -1
1 0 1 1 0 -1
1
Generator of the Alexander module
(0,0,-2,0,0,1)
the Blanchfield form on it
-14t^-2+43t^-1-60+43t-14t^2
57
First homology
of the double branched cover of 12n_0375
Z/57
-4 4
12n_0376
1

detected by
an unknotting move
1-4t+10t^2-19t^3+23t^4-19t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0376
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 0 1 0
-1 -1 0 -1 0 0 0 0
0 0 0 -1 -1 1 0 0
0 0 1 1 0 -1 1 1
0 0 0 0 0 0 1 0
-1 -1 1 0 0 0 1 1
1
Generator of the Alexander module
(0,0,6t-4t^2,3t-2t^2,t-t^2,1-t,0,0)
the Blanchfield form on it
-74t^-3+236t^-2-327t^-1+367-327t+236t^2-74t^3
91
First homology
of the double branched cover of 12n_0376
Z/91
-2 2
12n_0377
1

detected by
an unknotting move
1-4t+9t^2-11t^3+9t^4-4t^5+t^6
Seifert matrix of 12n_0377
0 0 1 0 0 -1
0 -1 0 0 0 0
1 -1 -2 0 0 1
0 0 1 1 1 -1
0 0 0 0 1 0
0 0 0 0 -1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+2t^-1-4+2t-t^2
39
First homology
of the double branched cover of 12n_0377
Z/39
2 2
12n_0378
1

detected by
an unknotting move
3-12t+24t^2-29t^3+24t^4-12t^5+3t^6
Seifert matrix of 12n_0378
-1 0 0 1 0 0
-1 -1 0 1 0 0
1 1 1 1 0 1
1 1 0 2 1 0
0 0 0 0 1 0
0 0 0 1 0 1
1
Generator of the Alexander module
(-6t-t^2-4t^3+16t^4-10t^5+14t^6-7t^7+t^8,-1+4t-3t^3+2t^4-4t^5+t^6,8-13t+6t^2+26t^3-67t^4+96t^5-103t^6+72t^7-42t^8+15t^9-2t^10,4-6t+t^2+14t^3-16t^4+35t^5-39t^6+38t^7-54t^8+34t^9-27t^10+13t^11-2t^12,1-4t+2t^2+t^3-t^4+14t^5-21t^6+18t^7-16t^8+7t^9-t^10,2-2t+t^2+10t^3-20t^4+18t^5-16t^6+7t^7-t^8)
the Blanchfield form on it
x
107
First homology
of the double branched cover of 12n_0378
Z/107
2 2
12n_0379
2

detected by
the Nakanishi index
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 12n_0379
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 0 0 -1 0 -1
0 0 -1 0 -1 -1
0 1 0 0 2 0
0 0 0 -1 0 0
2
63
First homology
of the double branched cover of 12n_0379
Z/21+Z/3
2 2
12n_0380
2

detected by
the Nakanishi index
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0380
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 0 -2 -1 0 -2
0 0 -1 0 -1 -1
0 1 0 0 2 0
0 0 -1 -1 0 -2
2
81
First homology
of the double branched cover of 12n_0380
Z/27+Z/3
0 0
12n_0381
1

detected by
an unknotting move
-3+15t-23t^2+15t^3-3t^4
Seifert matrix of 12n_0381
-5 -2 2 -3
-2 -2 1 -1
0 0 -2 -1
-4 -1 0 -3
1
Generator of the Alexander module
(-t+2t^2,2+2t-4t^2,0,-1+4t^2)
the Blanchfield form on it
-12t^-1+21-12t
59
First homology
of the double branched cover of 12n_0381
Z/59
-2 2
12n_0382
1

detected by
an unknotting move
-1+5t-7t^2+5t^3-t^4
Seifert matrix of 12n_0382
-3 -2 2 -5
-2 -2 1 -3
0 0 -2 1
-4 -3 4 -7
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
3t^-1-4+3t
19
First homology
of the double branched cover of 12n_0382
Z/19
-2 2
12n_0383
1

detected by
an unknotting move
-3+13t-19t^2+13t^3-3t^4
Seifert matrix of 12n_0383
-3 -6 -6 -5
-6 -10 -9 -9
-4 -6 -8 -7
-4 -7 -8 -7
1
Generator of the Alexander module
(1,0,-1,3)
the Blanchfield form on it
71t^-1-104+71t
51
First homology
of the double branched cover of 12n_0383
Z/51
-2 2
12n_0384
2

detected by
the signature
-3+13t-25t^2+31t^3-25t^4+13t^5-3t^6
Seifert matrix of 12n_0384
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 0 -2 -1 0 -1
0 -1 -2 -2 0 -1
0 0 0 -1 -1 -1
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(-t,0,1,0,t,0)
the Blanchfield form on it
-3t^-2+10t^-1-12+10t-3t^2
113
First homology
of the double branched cover of 12n_0384
Z/113
-4 4
12n_0385
1

detected by
an unknotting move
-1+7t-17t^2+23t^3-17t^4+7t^5-t^6
Seifert matrix of 12n_0385
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 0 -2 -1 0 -1
0 -1 -2 -2 0 -1
0 0 0 -1 1 -1
0 0 -1 -1 0 0
1
Generator of the Alexander module
(t,0,0,1,t,0)
the Blanchfield form on it
t^-1-2+t
73
First homology
of the double branched cover of 12n_0385
Z/73
0 0
12n_0386
4

detected by
the signature
-2+4t-3t^2-2t^3+5t^4-2t^5-3t^6+4t^7-2t^8
Seifert matrix of 12n_0386
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 -1
-1 -1 0 -1 0 0 0 0
0 0 -1 -1 -1 1 0 -1
0 0 1 1 0 -2 0 1
0 0 0 0 0 -1 -1 0
-1 -1 0 -1 0 0 0 -1
2
9
First homology
of the double branched cover of 12n_0386
Z/3+Z/3
-8 8
12n_0387
3

detected by
the signature
-1+5t-6t^2+2t^3+t^4+2t^5-6t^6+5t^7-t^8
Seifert matrix of 12n_0387
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 -1
-1 0 -1 0 -1 0 0 0
0 0 0 -1 -1 -1 0 -1
0 -1 0 0 0 -1 1 0
-1 0 -1 0 -1 0 0 -1
2
27
First homology
of the double branched cover of 12n_0387
Z/9+Z/3
-6 6
12n_0388
2

detected by
the Nakanishi index
-1+5t-10t^2+13t^3-10t^4+5t^5-t^6
Seifert matrix of 12n_0388
0 1 0 1 -1 2
0 -2 -1 -1 0 -2
0 0 -1 0 0 0
1 -2 -1 -2 1 -4
0 1 0 1 0 2
1 -2 -2 -3 1 -5
2
45
First homology
of the double branched cover of 12n_0388
Z/15+Z/3
0 0
12n_0389
2

detected by
the Nakanishi index
1-9t+24t^2-31t^3+24t^4-9t^5+t^6
Seifert matrix of 12n_0389
-2 0 -1 -1 -1 0
0 1 0 0 0 0
-2 0 -2 -1 -1 0
0 0 0 -1 0 0
-1 0 -1 -1 0 0
0 -1 0 0 -1 -1
2
99
First homology
of the double branched cover of 12n_0389
Z/33+Z/3
-2 2
12n_0390
1

detected by
an unknotting move
1-6t+14t^2-17t^3+14t^4-6t^5+t^6
Seifert matrix of 12n_0390
-1 0 0 0 0 0
0 2 0 1 0 1
-1 0 -1 0 0 0
-1 0 -1 1 0 0
0 0 0 -1 -1 -1
0 1 0 1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-1+3-t
59
First homology
of the double branched cover of 12n_0390
Z/59
-2 2
12n_0391
2

detected by
the Lickorish test
3-12t+26t^2-33t^3+26t^4-12t^5+3t^6
Seifert matrix of 12n_0391
-1 0 0 0 0 0
0 2 0 1 0 1
-1 0 -1 0 0 0
-1 0 -1 1 0 0
0 0 0 -1 1 -1
0 1 0 1 0 2
1
Generator of the Alexander module
(2+4t+t^2+2t^3,-2-3t+13t^2-9t^3+12t^4+2t^5+4t^6,-2-4t,1-t+4t^2,1+2t,6t-5t^2-4t^3)
the Blanchfield form on it
x
115
First homology
of the double branched cover of 12n_0391
Z/115
2 2
12n_0392
1

detected by
an unknotting move
1-8t+24t^2-33t^3+24t^4-8t^5+t^6
Seifert matrix of 12n_0392
1 0 0 0 0 0
-1 -1 0 -1 1 -1
0 0 -1 0 1 -1
-1 0 0 -1 1 0
0 0 0 0 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,2-t,-1,0,0)
the Blanchfield form on it
1
99
First homology
of the double branched cover of 12n_0392
Z/99
-2 2
12n_0393
2

detected by
A(F_2)
3-12t+19t^2-12t^3+3t^4
Seifert matrix of 12n_0393
-8 -3 -3 -6
-6 -3 -2 -4
-2 -1 0 -1
-7 -3 -2 -4
2
49
First homology
of the double branched cover of 12n_0393
Z/49
0 0
12n_0394
2

detected by
the Lickorish test
1-6t+11t^2-6t^3+t^4
Seifert matrix of 12n_0394
0 -1 -1 0
-2 -3 -2 0
0 -1 -2 1
-1 -1 0 0
2
25
First homology
of the double branched cover of 12n_0394
Z/25
0 0
12n_0395
2

detected by
the signature
-1+8t-18t^2+23t^3-18t^4+8t^5-t^6
Seifert matrix of 12n_0395
1 0 0 0 0 0
0 1 0 0 0 1
1 0 1 1 0 0
-1 -1 0 -1 0 0
1 1 0 1 1 1
0 0 0 0 0 1
1 or 2
77
First homology
of the double branched cover of 12n_0395
Z/77
4 4
12n_0396
1

detected by
an unknotting move
1-7t+16t^2-19t^3+16t^4-7t^5+t^6
Seifert matrix of 12n_0396
1 0 0 0 0 0
0 1 0 0 0 1
1 0 0 1 -1 0
-1 -1 0 -1 0 0
1 1 -1 1 -2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,-1+t-t^2,0,-2+2t-t^2,0)
the Blanchfield form on it
-t^-2+4t^-1-4+4t-t^2
67
First homology
of the double branched cover of 12n_0396
Z/67
2 2
12n_0397
2

detected by
the Nakanishi index
-1+5t-11t^2+15t^3-11t^4+5t^5-t^6
Seifert matrix of 12n_0397
0 0 0 -1 0 0
-1 -1 0 -1 1 0
-1 0 -1 -1 0 0
-2 -1 0 -1 0 0
0 0 0 0 1 1
0 0 0 0 0 1
2
49
First homology
of the double branched cover of 12n_0397
Z/7+Z/7
0 0
12n_0398
2

detected by
the signature
-1+4t-4t^2+3t^3-4t^4+4t^5-t^6
Seifert matrix of 12n_0398
1 0 1 0 0 0
-1 -1 0 -1 1 0
0 0 1 0 0 0
-1 -1 1 0 0 0
0 0 0 0 1 1
0 0 0 0 0 1
1 or 2
21
First homology
of the double branched cover of 12n_0398
Z/21
4 4
12n_0399
1

detected by
an unknotting move
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 12n_0399
1 0 1 0 0 0
-1 0 0 -1 1 0
0 0 1 0 0 0
-1 -1 1 0 0 0
0 0 0 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,1)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
81
First homology
of the double branched cover of 12n_0399
Z/81
0 0
12n_0400
1

detected by
an unknotting move
1-8t+23t^2-31t^3+23t^4-8t^5+t^6
Seifert matrix of 12n_0400
2 0 1 0 1 0
0 -1 0 -1 -1 0
0 0 0 0 1 0
1 0 1 1 1 0
1 0 1 0 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,-t,0,t,1,0)
the Blanchfield form on it
t^-1-4+t
95
First homology
of the double branched cover of 12n_0400
Z/95
2 2
12n_0401
2

detected by
the Lickorish test
1-7t+21t^2-29t^3+21t^4-7t^5+t^6
Seifert matrix of 12n_0401
-1 0 0 0 0 -1
0 1 1 2 1 0
0 1 1 1 1 -1
0 1 0 0 1 0
0 2 1 2 1 0
0 0 0 0 0 -1
1 or 2
87
First homology
of the double branched cover of 12n_0401
Z/87
-2 2
12n_0402
2

detected by
the Nakanishi index
1+t-3t^2+3t^3-3t^4+t^5+t^6
Seifert matrix of 12n_0402
1 0 0 0 0 0
1 1 0 1 0 0
1 0 1 0 0 -1
1 0 0 1 0 0
1 1 0 1 1 0
1 0 0 0 0 1
2
9
First homology
of the double branched cover of 12n_0402
Z/3+Z/3
4 4
12n_0403
2

detected by
the Nakanishi index
-1+3t-t^2-t^3-t^4+3t^5-t^6
Seifert matrix of 12n_0403
1 0 0 0 0 0
1 0 0 0 -1 -1
1 0 1 0 0 -1
1 -1 0 0 -1 -1
1 0 0 0 0 -1
1 -1 0 -1 -1 -2
2
9
First homology
of the double branched cover of 12n_0403
Z/3+Z/3
4 4
12n_0404
1

detected by
an unknotting move
2+t-5t^2+t^3+2t^4
Seifert matrix of 12n_0404
1 0 0 0
-1 2 0 0
1 0 1 -1
1 0 0 1
1
Generator of the Alexander module
(0,-1,t,1)
the Blanchfield form on it
t^-1-2+t
3
First homology
of the double branched cover of 12n_0404
Z/3
2 2
12n_0405
2

detected by
the signature
1-6t+13t^2-12t^3+9t^4-12t^5+13t^6-6t^7+t^8
Seifert matrix of 12n_0405
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 0 0 -1 0
0 -1 0 -1 1 -1 -1 1
0 0 0 -1 0 -1 -1 0
-1 0 -1 0 0 0 -1 0
0 -1 0 -1 0 -1 0 1
1 or 2
73
First homology
of the double branched cover of 12n_0405
Z/73
-4 4
12n_0406
3

detected by
the signature
5-13t+16t^2-15t^3+16t^4-13t^5+5t^6
Seifert matrix of 12n_0406
-1 0 0 0 0 0
0 -2 0 0 -1 -1
-1 0 -1 0 0 0
-1 -1 -1 -1 -1 0
0 -1 0 0 -2 -1
1 0 1 0 -1 -2
1 or 2
83
First homology
of the double branched cover of 12n_0406
Z/83
-6 6
12n_0407
2

detected by
the signature
-1+5t-8t^2+9t^3-8t^4+5t^5-t^6
Seifert matrix of 12n_0407
-1 0 0 0 0 0
0 0 0 0 -1 -1
-1 0 -1 0 0 0
-1 -1 -1 -1 -1 0
0 -1 0 0 -2 -1
1 0 1 0 -1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
37
First homology
of the double branched cover of 12n_0407
Z/37
-4 4
12n_0408
1

detected by
an unknotting move
-1+9t-24t^2+33t^3-24t^4+9t^5-t^6
Seifert matrix of 12n_0408
-1 0 0 0 0 0
0 0 0 1 1 0
-1 0 -1 0 0 0
-1 0 -1 1 0 0
0 1 0 1 2 1
1 1 1 0 1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-3t^-2+9t^-1-13+9t-3t^2
101
First homology
of the double branched cover of 12n_0408
Z/101
0 0
12n_0409
2

detected by
the Lickorish test
1-3t+9t^2-13t^3+9t^4-3t^5+t^6
Seifert matrix of 12n_0409
-1 1 -1 0 0 0
0 1 1 0 1 0
0 1 0 1 0 1
0 0 0 1 0 1
0 1 1 1 2 1
0 0 0 0 0 1
1 or 2
39
First homology
of the double branched cover of 12n_0409
Z/39
2 2
12n_0410
2

detected by
the Lickorish test
2-10t+26t^2-35t^3+26t^4-10t^5+2t^6
Seifert matrix of 12n_0410
-1 1 -1 0 0 0
0 -3 1 0 -1 0
0 1 -1 1 0 1
0 0 0 1 0 1
0 -1 1 1 -1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(42-44t+21t^2-750t^3+2306t^4-3140t^5+2210t^6-800t^7+120t^8,-42+72t+20t^2+312t^3-1138t^4+1400t^5-664t^6+96t^7,-35+135t-70t^2-56t^3-88t^4+354t^5-208t^6+24t^7,10-4t-42t^2+64t^3-24t^4,-7+26t+36t^2-194t^3+258t^4-136t^5+24t^6,7+18t-188t^2+388t^3-370t^4+160t^5-24t^6)
the Blanchfield form on it
x
111
First homology
of the double branched cover of 12n_0410
Z/111
-2 2
12n_0411
1

detected by
an unknotting move
5-9t+5t^2
Seifert matrix of 12n_0411
11 -3
-2 1
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
t^-1-2+t
19
First homology
of the double branched cover of 12n_0411
Z/19
2 2
12n_0412
1

detected by
an unknotting move
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 12n_0412
0 0 -1 0 1 -1
1 -1 0 0 1 0
-1 -1 0 0 0 0
1 1 0 1 1 0
0 0 0 0 1 0
-1 0 -1 0 0 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-1
75
First homology
of the double branched cover of 12n_0412
Z/75
2 2
12n_0413
2

detected by
the Lickorish test
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 12n_0413
-1 0 1 1 0 1
0 2 1 1 1 1
0 0 -1 -1 1 -1
0 1 0 -1 1 0
0 0 0 0 1 0
0 0 0 -1 1 -1
1
Generator of the Alexander module
(1+t,1,0,0,0,0)
the Blanchfield form on it
4t^-2-10t^-1+15-10t+4t^2
75
First homology
of the double branched cover of 12n_0413
Z/75
-2 2
12n_0414
2

detected by
the Nakanishi index
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 12n_0414
1 1 -1 -1
2 0 0 0
-1 -1 0 0
-1 0 -1 0
2
25
First homology
of the double branched cover of 12n_0414
Z/5+Z/5
0 0
12n_0415
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 12n_0415
-1 0 -1 -1 -1 0
0 1 0 0 0 0
0 -1 -2 -2 -2 0
0 0 -1 -2 -1 0
0 -1 -1 -2 -2 0
0 1 1 1 1 1
1
Generator of the Alexander module
(-t,0,1,1,1,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
103
First homology
of the double branched cover of 12n_0415
Z/103
-2 2
12n_0416
2

detected by
the signature
-1+4t-10t^2+15t^3-17t^4+15t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0416
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 1 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 0 1 0 0 1
-1 -1 0 0 1 -1 0 1
0 0 0 0 0 -1 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-6t^-1+7-6t+3t^2-t^3
77
First homology
of the double branched cover of 12n_0416
Z/77
-4 4
12n_0417
3

detected by
the signature
-1+4t^2-9t^3+11t^4-9t^5+4t^6-t^8
Seifert matrix of 12n_0417
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 1 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 0 0 1 -1 0 1
0 0 0 0 0 -1 -1 0
0 0 0 0 -1 0 0 -1
1 or 2
35
First homology
of the double branched cover of 12n_0417
Z/35
-6 6
12n_0418
3

detected by
the signature
1-4t+4t^2-t^3-t^4-t^5+4t^6-4t^7+t^8
Seifert matrix of 12n_0418
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 0
0 0 -1 -1 0 0 0 -1
0 0 0 0 1 0 0 0
-1 -1 0 0 1 -1 0 0
0 0 0 0 0 -1 -1 0
-1 -1 -1 0 1 0 0 -1
1 or 2
19
First homology
of the double branched cover of 12n_0418
Z/19
-6 6
12n_0419
3

detected by
the signature
1-4t+3t^2+3t^3-7t^4+3t^5+3t^6-4t^7+t^8
Seifert matrix of 12n_0419
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 -1 0
-1 -1 0 -1 0 0 0 0
0 0 -1 0 -1 -1 -1 0
-1 -1 0 0 0 -1 -1 0
0 0 0 0 0 0 1 0
0 0 0 -1 0 0 1 -1
1
Generator of the Alexander module
(-6t^4+8t^6-4t^8+2t^9,1+t^2+2t^3+32t^4+66t^5-36t^6-247t^7-60t^8+322t^9-5t^10-146t^11+68t^12,8t^2+11t^3-4t^4-54t^5+2t^6+50t^7+t^8-26t^9+12t^10,-4t-2t^2-2t^3-t^4+30t^5-17t^6+37t^7-103t^8+118t^9-74t^10+28t^11-6t^12,16t^2+25t^3-8t^4-124t^5+4t^6+118t^7+t^8-60t^9+28t^10,2t-10t^2-19t^3+9t^4+37t^5+19t^6-50t
the Blanchfield form on it
x
3
First homology
of the double branched cover of 12n_0419
Z/3
-6 6
12n_0420
2

detected by
the Nakanishi index
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 12n_0420
1 0 0 0 0 -1
0 -1 0 0 0 0
0 -1 -2 0 -1 -1
1 0 -1 1 -1 -1
0 -1 -1 0 0 0
0 -1 -1 0 -1 -2
2
81
First homology
of the double branched cover of 12n_0420
Z/27+Z/3
0 0
12n_0421
1

detected by
an unknotting move
-2+11t-27t^2+37t^3-27t^4+11t^5-2t^6
Seifert matrix of 12n_0421
-1 0 0 1 -1 1
0 2 0 0 0 0
0 1 -1 0 0 0
0 1 1 1 0 1
0 -1 -1 0 -1 0
0 1 1 0 0 1
1 or 2
117
First homology
of the double branched cover of 12n_0421
Z/117
0 0
12n_0422
1

detected by
an unknotting move
-2+11t-27t^2+37t^3-27t^4+11t^5-2t^6
Seifert matrix of 12n_0422
1 0 0 1 0 1
0 1 -1 -1 0 -1
0 0 -2 -1 0 -1
0 0 0 -1 0 0
1 -1 -1 0 1 0
0 0 0 -1 0 -1
1
Generator of the Alexander module
(8-8t-240t^2+1048t^3-784t^4-544t^5+928t^6-416t^7+64t^8,-3+3t+90t^2-393t^3+294t^4+204t^5-348t^6+156t^7-24t^8,-4+4t+120t^2-524t^3+392t^4+272t^5-464t^6+208t^7-32t^8,0,-4+2t+108t^2-337t^3-149t^4+668t^5-192t^6-300t^7+212t^8-40t^9,-2+t-3t^3-58t^4+40t^5+36t^6-36t^7+8t^8)
the Blanchfield form on it
x
117
First homology
of the double branched cover of 12n_0422
Z/117
0 0
12n_0423
2

detected by
the Lickorish test
1-3t+3t^2-t^3+3t^4-3t^5+t^6
Seifert matrix of 12n_0423
-1 0 0 0 -1 -1
0 1 0 0 0 0
0 1 1 1 0 0
0 1 1 1 0 1
0 0 1 2 1 1
0 1 1 2 0 0
1 or 2
15
First homology
of the double branched cover of 12n_0423
Z/15
2 2
12n_0424
1

detected by
an unknotting move
-1+5t-12t^2+19t^3-21t^4+19t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0424
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 1 0 0 1 0 1 0
-1 -1 -1 0 -1 -1 -1 0
0 0 0 0 0 0 1 0
0 -1 0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,-1,1,-1,0,1,0,1)
the Blanchfield form on it
1
95
First homology
of the double branched cover of 12n_0424
Z/95
-2 2
12n_0425
2

detected by
the signature
1-4t+7t^2-4t^3+t^4-4t^5+7t^6-4t^7+t^8
Seifert matrix of 12n_0425
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 1 0 0 1 0 1 0
-1 -1 -1 0 -1 1 -1 1
0 0 0 0 0 0 1 0
0 -1 0 0 0 0 -1 1
1 or 2
33
First homology
of the double branched cover of 12n_0425
Z/33
4 4
12n_0426
3

detected by
the signature
1-3t^2+4t^3-3t^4+4t^5-3t^6+t^8
Seifert matrix of 12n_0426
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 -1 0 -1 -1 -1 0
0 -1 0 0 -1 0 -1 0
0 -1 0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,1-7t^2+2t^4,-1+4t-2t^2,0,0,0,-3-2t+2t^2)
the Blanchfield form on it
117t^-3-242t^-2+282t^-1-250+282t-242t^2+117t^3
15
First homology
of the double branched cover of 12n_0426
Z/15
-6 6
12n_0427
2

detected by
the signature
1-5t+14t^2-23t^3+27t^4-23t^5+14t^6-5t^7+t^8
Seifert matrix of 12n_0427
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 -1 0 -1 1 -1 1
0 -1 0 0 -1 0 -1 0
0 -1 0 0 0 0 -1 1
1
Generator of the Alexander module
(0,1,-t,0,0,1-t,1,0)
the Blanchfield form on it
t^-3-5t^-2+13t^-1-17+13t-5t^2+t^3
113
First homology
of the double branched cover of 12n_0427
Z/113
-4 4
12n_0428
3

detected by
the signature
-1+4t-5t^2+4t^3-3t^4+4t^5-5t^6+4t^7-t^8
Seifert matrix of 12n_0428
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 -1 0 -1 -1 -1 0
0 -1 0 0 -1 0 -1 0
0 -1 0 0 0 -1 -1 -1
1 or 2
31
First homology
of the double branched cover of 12n_0428
Z/31
-6 6
12n_0429
1

detected by
an unknotting move
-4+18t-27t^2+18t^3-4t^4
Seifert matrix of 12n_0429
10 6 3 6
3 1 1 2
4 2 2 3
5 3 2 4
1
Generator of the Alexander module
(3,0,1,1)
the Blanchfield form on it
t^-1-2+t
71
First homology
of the double branched cover of 12n_0429
Z/71
2 2
12n_0431
1

detected by
an unknotting move
-1+8t-24t^2+35t^3-24t^4+8t^5-t^6
Seifert matrix of 12n_0431
1 0 0 0 0 0
0 1 0 0 0 0
1 0 0 1 -1 0
-1 -1 0 -1 0 0
1 0 -1 1 -2 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,-1,0,1)
the Blanchfield form on it
-t^-1+3-t
101
First homology
of the double branched cover of 12n_0431
Z/101
0 0
12n_0432
2

detected by
the signature
3-4t+3t^2-4t^3+3t^4
Seifert matrix of 12n_0432
1 0 0 0
-1 2 0 1
1 1 1 1
0 1 0 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
2t^-2-3t^-1+2-3t+2t^2
17
First homology
of the double branched cover of 12n_0432
Z/17
4 4
12n_0433
1

detected by
an unknotting move
-1+2t+4t^2-9t^3+4t^4+2t^5-t^6
Seifert matrix of 12n_0433
1 0 0 0 0 0
0 1 1 1 1 -1
1 0 1 0 0 -1
1 0 0 1 1 -1
1 0 0 0 1 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,t,0,0)
the Blanchfield form on it
-t^-2+5t^-1-8+5t-t^2
11
First homology
of the double branched cover of 12n_0433
Z/11
2 2
12n_0434
1

detected by
an unknotting move
-1+6t-15t^2+21t^3-15t^4+6t^5-t^6
Seifert matrix of 12n_0434
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 0 -1 -1 -1
1 -1 -1 0 0 -1
1 -1 -1 -1 0 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,5-6t-2t^2,1+4t-3t^2,1+t-4t^2-8t^3,2-4t,1)
the Blanchfield form on it
-136t^-2+358t^-1-403+358t-136t^2
65
First homology
of the double branched cover of 12n_0434
Z/65
0 0
12n_0435
1

detected by
an unknotting move
-1+6t-13t^2+17t^3-13t^4+6t^5-t^6
Seifert matrix of 12n_0435
0 -1 0 0 -1 0
-2 -1 0 0 -1 -1
0 0 1 0 0 -1
-1 -1 0 -1 -1 0
-1 -1 0 0 0 0
-1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,t,-1,0,1)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
57
First homology
of the double branched cover of 12n_0435
Z/57
0 2
12n_0436
2

detected by
the signature
-1+5t-6t^2+5t^3-6t^4+5t^5-t^6
Seifert matrix of 12n_0436
1 0 0 1 0 0
-1 0 0 1 0 -1
0 0 1 0 0 -1
0 0 0 1 0 0
0 0 0 1 1 0
-1 -1 0 0 -1 -1
2
29
First homology
of the double branched cover of 12n_0436
Z/29
4 4
12n_0437
1

detected by
an unknotting move
1+t-8t^2+13t^3-8t^4+t^5+t^6
Seifert matrix of 12n_0437
-1 1 0 0 0 0
0 -3 -1 0 -1 0
0 -1 0 1 -1 1
0 0 0 1 0 1
0 -1 0 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(2-t,0,2,1,1,0)
the Blanchfield form on it
2t^-1-3+2t
29
First homology
of the double branched cover of 12n_0437
Z/29
0 0
12n_0438
2

detected by
the signature
-1+3t-4t^2+5t^3-4t^4+3t^5-t^6
Seifert matrix of 12n_0438
-2 -1 -1 0 -1 -1
0 -1 -1 0 0 0
0 0 -1 0 0 0
-1 -1 -1 -1 -1 0
-2 -1 -1 0 -1 0
-1 -1 0 0 0 0
1
Generator of the Alexander module
(0,0,0,1+t-t^4,0,t^2)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
21
First homology
of the double branched cover of 12n_0438
Z/21
-4 4
12n_0439
1

detected by
an unknotting move
1-t+t^3-t^5+t^6
Seifert matrix of 12n_0439
-1 0 0 1 0 -1
1 0 0 1 1 0
1 1 1 1 1 0
0 0 0 1 0 0
-1 0 0 1 0 0
-1 -1 0 0 0 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-1-2+t
3
First homology
of the double branched cover of 12n_0439
Z/3
2 2
12n_0440
2

detected by
the Nakanishi index
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0440
-1 0 2 2 2 1
0 0 1 1 1 0
0 2 -6 -6 -7 -4
0 2 -7 -6 -7 -4
0 2 -6 -6 -6 -4
0 0 -2 -2 -2 -1
2
81
First homology
of the double branched cover of 12n_0440
Z/9+Z/9
0 0
12n_0441
2

detected by
the signature
-1+9t-22t^2+29t^3-22t^4+9t^5-t^6
Seifert matrix of 12n_0441
-16 -11 -8 -15 -8 -4
-12 -8 -6 -12 -6 -3
-5 -4 -4 -5 -3 -1
-16 -11 -8 -16 -8 -4
-7 -5 -4 -7 -4 -2
-5 -4 -3 -5 -3 -2
1 or 2
93
First homology
of the double branched cover of 12n_0441
Z/93
-4 4
12n_0442
2

detected by
the Lickorish test
-3+10t-13t^2+10t^3-3t^4
Seifert matrix of 12n_0442
-3 -2 -2 -1
-1 -2 -1 0
-3 -2 -2 0
-1 -1 0 0
2
39
First homology
of the double branched cover of 12n_0442
Z/39
-2 2
12n_0443
1

detected by
an unknotting move
3-8t+11t^2-8t^3+3t^4
Seifert matrix of 12n_0443
0 1 1 -1
2 1 2 0
0 1 1 0
-1 -1 0 0
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
t^-1-2+t
33
First homology
of the double branched cover of 12n_0443
Z/33
0 2
12n_0444
1

detected by
an unknotting move
-2+7t-9t^2+7t^3-2t^4
Seifert matrix of 12n_0444
-1 0 2 1
0 0 1 0
0 2 -5 -4
0 0 -2 -1
1 or 2
27
First homology
of the double branched cover of 12n_0444
Z/27
-2 2
12n_0445
2

detected by
the signature
-2+13t-30t^2+39t^3-30t^4+13t^5-2t^6
Seifert matrix of 12n_0445
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 -1 -2 0 -2 1
0 -1 -1 -1 -1 1
0 0 -1 0 -2 1
0 -1 0 0 0 -1
1 or 2
129
First homology
of the double branched cover of 12n_0445
Z/129
-4 4
12n_0446
1

detected by
an unknotting move
-1+2t+3t^2-7t^3+3t^4+2t^5-t^6
Seifert matrix of 12n_0446
-2 0 0 -1 -1 -2
0 -1 0 0 0 0
-2 0 0 -1 -1 -1
0 0 0 -1 0 -1
-1 0 0 0 -1 -1
0 1 1 0 0 0
1
Generator of the Alexander module
(0,0,1,-t,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
7
First homology
of the double branched cover of 12n_0446
Z/7
-2 2
12n_0447
1

detected by
an unknotting move
-2+8t-16t^2+21t^3-16t^4+8t^5-2t^6
Seifert matrix of 12n_0447
0 1 1 0 0 1
0 -1 0 0 0 0
1 0 0 1 0 -1
-1 1 1 0 0 1
-1 0 1 -1 -1 1
1 -1 -2 1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-2+6t^-1-7+6t-2t^2
73
First homology
of the double branched cover of 12n_0447
Z/73
0 0
12n_0448
1

detected by
an unknotting move
1-6t+14t^2-21t^3+25t^4-21t^5+14t^6-6t^7+t^8
Seifert matrix of 12n_0448
-1 0 -1 -1 0 0 -1 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 -1 0
-1 0 0 -1 1 1 -1 1
0 0 0 0 0 1 0 0
0 1 -1 0 0 0 -1 0
-1 0 0 -1 0 1 0 1
1
Generator of the Alexander module
(0,0,0,0,3-t+2t^2-t^3,1+2t^2-t^3,0,1+2t^2-t^3)
the Blanchfield form on it
t^-2-3t^-1+1-3t+t^2
109
First homology
of the double branched cover of 12n_0448
Z/109
0 2
12n_0449
1

detected by
an unknotting move
1-4t+8t^2-9t^3+8t^4-4t^5+t^6
Seifert matrix of 12n_0449
-1 0 -1 0 -1 0
0 -1 0 -1 0 0
0 0 0 0 -1 0
0 0 0 -1 0 0
0 0 -1 -1 0 -1
0 1 1 1 0 2
1
Generator of the Alexander module
(-t,0,1,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
35
First homology
of the double branched cover of 12n_0449
Z/35
-2 2
12n_0450
1

detected by
an unknotting move
1-8t+23t^2-31t^3+23t^4-8t^5+t^6
Seifert matrix of 12n_0450
-1 0 -1 0 -1 0
0 -1 0 -1 0 0
0 0 -2 0 -1 -1
0 0 0 -1 0 0
0 0 -1 -1 0 -1
0 1 0 1 0 1
1
Generator of the Alexander module
(-11t+10t^2+10t^3-7t^4+t^5,0,-21t+7t^2,1-9t+6t^2-t^3,3-13t-8t^2+7t^3-t^4,-3+t)
the Blanchfield form on it
-2t^-2+9t^-1-12+9t-2t^2
95
First homology
of the double branched cover of 12n_0450
Z/95
-2 2
12n_0451
2

detected by
the Lickorish test
1-3t+8t^2-11t^3+8t^4-3t^5+t^6
Seifert matrix of 12n_0451
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 0 0 0 -1 0
0 1 0 1 0 0
0 0 -1 -1 0 -1
0 1 1 1 0 2
1 or 2
35
First homology
of the double branched cover of 12n_0451
Z/35
2 2
12n_0452
1

detected by
an unknotting move
-4+14t-19t^2+14t^3-4t^4
Seifert matrix of 12n_0452
-6 -6 -4 -5
-4 -3 -2 -4
-5 -4 -4 -4
-4 -5 -2 -4
1
Generator of the Alexander module
(2,1,1,2)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
55
First homology
of the double branched cover of 12n_0452
Z/55
-2 2
12n_0453
3

detected by
the signature
5-15t+24t^2-27t^3+24t^4-15t^5+5t^6
Seifert matrix of 12n_0453
-1 0 -1 0 -1 0
0 -1 0 -1 0 0
0 0 -2 0 -1 -1
0 0 0 -1 0 0
0 0 -1 -1 -2 0
0 1 0 1 1 -2
1 or 2
115
First homology
of the double branched cover of 12n_0453
Z/115
-6 6
12n_0454
1

detected by
an unknotting move
1-4t+11t^2-15t^3+11t^4-4t^5+t^6
Seifert matrix of 12n_0454
-1 1 -1 0 -1 0
0 1 1 0 1 0
0 1 0 1 -1 1
0 0 0 1 0 1
0 1 0 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1-t,0,0,-1,0,0)
the Blanchfield form on it
t^-1-2+t
47
First homology
of the double branched cover of 12n_0454
Z/47
2 2
12n_0455
2

detected by
the signature
-3+12t-21t^2+25t^3-21t^4+12t^5-3t^6
Seifert matrix of 12n_0455
-1 1 -1 0 -1 0
0 1 1 0 1 0
0 1 -2 0 -2 0
0 0 -1 -1 -1 0
0 1 -1 0 -2 0
0 0 -1 -1 -1 -1
1
Generator of the Alexander module
(t-2t^2+3t^3-3t^4+t^5,t-2t^2+3t^3-3t^4+t^5,-2t+4t^2-6t^3+6t^4-2t^5,0,1-3t+6t^2-7t^3+6t^4-2t^5,2-2t^4+t^5)
the Blanchfield form on it
4t^-7-102t^-6+650t^-5-2249t^-4+5316t^-3-9434t^-2+13128t^-1-14624+13128t-9434t^2+5316t^3-2249t^4+650t^5-102t^6+4t^7
97
First homology
of the double branched cover of 12n_0455
Z/97
-4 4
12n_0456
1

detected by
an unknotting move
1-5t^2+9t^3-5t^4+t^6
Seifert matrix of 12n_0456
-1 1 -1 0 -1 0
0 -3 1 0 1 0
0 1 0 1 -1 1
0 0 0 1 0 1
0 1 0 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,1,0,0,0)
the Blanchfield form on it
t^-1-2+t
17
First homology
of the double branched cover of 12n_0456
Z/17
0 0
12n_0457
1

detected by
an unknotting move
3-5t+3t^2
Seifert matrix of 12n_0457
3 3
4 5
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
-1
11
First homology
of the double branched cover of 12n_0457
Z/11
2 2
12n_0458
1

detected by
an unknotting move
1-6t+16t^2-26t^3+31t^4-26t^5+16t^6-6t^7+t^8
Seifert matrix of 12n_0458
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 -1
0 -1 0 0 1 -1 1 0
0 0 0 0 0 -1 0 0
0 -1 0 0 0 -1 1 0
0 0 0 0 1 -1 1 1
1
Generator of the Alexander module
(-2t^2-4t^3+4t^4-6t^5+6t^6-2t^7,-t^2,0,1+t-2t^2+3t^3-3t^4+t^5,-t^2-2t^3+2t^4-3t^5+3t^6-t^7,-4t^3,0,-2t^3)
the Blanchfield form on it
x
129
First homology
of the double branched cover of 12n_0458
Z/129
0 2
12n_0459
2

detected by
the signature
1-6t+15t^2-20t^3+21t^4-20t^5+15t^6-6t^7+t^8
Seifert matrix of 12n_0459
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 -1 1
0 -1 0 0 -1 -1 -1 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 -1 -1 0
0 0 0 0 -1 0 0 1
1 or 2
105
First homology
of the double branched cover of 12n_0459
Z/105
-4 4
12n_0460
2

detected by
the Nakanishi index
1-6t+15t^2-19t^3+15t^4-6t^5+t^6
Seifert matrix of 12n_0460
1 0 0 0 0 0
0 1 0 -1 0 -1
1 0 -2 -1 0 -1
1 0 -2 -2 0 -1
0 1 -1 -1 1 -1
1 0 -1 -1 0 0
2
63
First homology
of the double branched cover of 12n_0460
Z/21+Z/3
2 2
12n_0461
1

detected by
an unknotting move
-1+7t-20t^2+29t^3-20t^4+7t^5-t^6
Seifert matrix of 12n_0461
0 0 -1 0 -1 0
0 0 -1 0 0 0
-1 0 0 -1 -1 0
0 0 0 -1 0 0
-1 0 -2 -1 -1 -1
-1 1 0 -1 -1 0
1
Generator of the Alexander module
(0,0,0,2-t,0,1)
the Blanchfield form on it
1
85
First homology
of the double branched cover of 12n_0461
Z/85
0 0
12n_0462
2

detected by
the Lickorish test
1-6t+11t^2-6t^3+t^4
Seifert matrix of 12n_0462
-2 0 1 1
0 0 0 -1
0 -1 0 -1
1 0 -1 1
2
25
First homology
of the double branched cover of 12n_0462
Z/25
0 0
12n_0463
1

detected by
an unknotting move
-1+7t-18t^2+25t^3-18t^4+7t^5-t^6
Seifert matrix of 12n_0463
2 0 0 1 -1 1
0 -1 -1 0 0 0
0 0 1 0 0 0
1 0 0 0 0 1
0 -1 -1 0 -1 0
0 1 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
77
First homology
of the double branched cover of 12n_0463
Z/77
0 0
12n_0464
1

detected by
an unknotting move
-1+4t-5t^2+4t^3-t^4
Seifert matrix of 12n_0464
0 0 -1 -1
0 -1 0 -1
0 0 -1 0
-1 0 -1 -2
1
Generator of the Alexander module
(0,-t,0,1)
the Blanchfield form on it
1
15
First homology
of the double branched cover of 12n_0464
Z/15
-2 2
12n_0465
1

detected by
an unknotting move
-1+6t-13t^2+15t^3-13t^4+15t^5-13t^6+6t^7-t^8
Seifert matrix of 12n_0465
-1 1 -1 0 0 0 1 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 -1 0 0 -1 0
-1 0 0 0 1 -1 0 1
-1 1 -1 1 0 -1 1 0
0 -1 0 0 0 0 -1 0
0 0 0 0 0 -1 0 1
1
Generator of the Alexander module
(0,t-3t^2+2t^4-2t^5+2t^6,-1+t+t^2+2t^3-4t^4+2t^5-2t^6,t-3t^2+2t^4-2t^5+2t^6,2t+2t^2-6t^3+4t^5-4t^6+4t^7,4t-3t^2+3t^3-6t^4+6t^5-2t^6+2t^7,t-3t^2+2t^4-2t^5+2t^6,-t+7t^2-9t^3+4t^4-2t^6+2t^7)
the Blanchfield form on it
x
83
First homology
of the double branched cover of 12n_0465
Z/83
-2 2
12n_0466
2

detected by
the signature
1-3t+7t^2-10t^3+11t^4-10t^5+7t^6-3t^7+t^8
Seifert matrix of 12n_0466
-1 0 -1 -1 -1 0 -1 -1
0 1 0 0 0 1 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 1 -1 -1 0 1 -1 -1
0 0 0 0 0 1 0 0
0 0 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 0
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
2t^-3-4t^-2+6t^-1-7+6t-4t^2+2t^3
53
First homology
of the double branched cover of 12n_0466
Z/53
4 4
12n_0467
1

detected by
an unknotting move
-1+3t-5t^2+8t^3-9t^4+8t^5-5t^6+3t^7-t^8
Seifert matrix of 12n_0467
-1 0 -1 -1 -1 0 -1 -1
0 1 0 0 0 1 0 0
0 0 -2 -2 -1 0 -2 -2
0 0 -1 -2 -1 0 -1 -2
0 1 -1 -1 0 1 -1 -1
0 0 0 0 0 1 0 0
0 0 -1 -2 -1 0 -2 -2
0 0 -1 -1 -1 0 -1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-4t^-1+5-4t+3t^2-t^3
43
First homology
of the double branched cover of 12n_0467
Z/43
-2 2
12n_0468
1

detected by
an unknotting move
1-3t+5t^2-6t^3+7t^4-6t^5+5t^6-3t^7+t^8
Seifert matrix of 12n_0468
-1 0 -1 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 0 -1 -1 -2 0 -1 -1
0 -1 0 0 -1 -1 0 0
0 0 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 0
1
Generator of the Alexander module
(1,0,0,0,0,1,0,0)
the Blanchfield form on it
2t^-3-5t^-2+6t^-1-4+6t-5t^2+2t^3
37
First homology
of the double branched cover of 12n_0468
Z/37
0 2
12n_0469
2

detected by
the Lickorish test
2-6t+12t^2-15t^3+12t^4-6t^5+2t^6
Seifert matrix of 12n_0469
-1 0 -1 1 -1 0
0 1 0 0 0 1
0 0 0 1 -1 0
0 0 0 1 1 0
0 1 -1 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
55
First homology
of the double branched cover of 12n_0469
Z/55
2 2
12n_0470
1

detected by
an unknotting move
-2+6t-8t^2+9t^3-8t^4+6t^5-2t^6
Seifert matrix of 12n_0470
-1 0 -1 1 -1 0
0 1 0 0 0 1
0 0 -2 2 -1 0
0 0 1 -3 1 0
0 1 -1 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-4+4t-3t^2+t^3
41
First homology
of the double branched cover of 12n_0470
Z/41
0 2
12n_0471
1

detected by
an unknotting move
2-8t+16t^2-19t^3+16t^4-8t^5+2t^6
Seifert matrix of 12n_0471
-1 0 -1 1 -1 0
0 -1 0 0 -1 0
0 0 0 1 -1 0
0 0 0 1 1 0
0 0 -1 1 -2 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(1,0,0,0,0,1)
the Blanchfield form on it
4t^-2-14t^-1+22-14t+4t^2
71
First homology
of the double branched cover of 12n_0471
Z/71
-2 2
12n_0472
4

detected by
the signature
-1+t-2t^3+4t^4-5t^5+4t^6-2t^7+t^9-t^10
Seifert matrix of 12n_0472
-1 0 0 0 0 0 0 0 0 0
0 -1 0 -1 -1 -1 0 -1 -1 -1
-1 0 -1 0 0 0 0 0 0 0
-1 0 -1 -1 -1 -1 0 0 -1 -1
-1 0 -1 0 -1 -1 0 0 0 -1
-1 0 -1 0 0 -1 0 0 0 0
0 -1 0 -1 -1 -1 -1 -1 -1 -1
0 0 0 -1 -1 -1 0 -1 -1 -1
-1 0 -1 0 -1 -1 0 0 -1 -1
-1 0 -1 0 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-4+t^-3-t^-1+1-t+t^3-t^4
13
First homology
of the double branched cover of 12n_0472
Z/13
-8 8
12n_0473
4

detected by
the signature
2-3t+t^2+3t^3-5t^4+3t^5+t^6-3t^7+2t^8
Seifert matrix of 12n_0473
-1 0 0 0 0 0 0 0
0 -1 0 -1 1 -1 0 -1
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 1 -1 0 0
1 0 1 0 -2 1 0 0
-1 0 -1 0 0 -1 0 0
0 -1 0 -1 1 -1 -1 -1
0 0 0 -1 1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,-2t,0,0,0)
the Blanchfield form on it
-5t^-4+8t^-3-3t^-2-7t^-1+12-7t-3t^2+8t^3-5t^4
1
First homology
of the double branched cover of 12n_0473
0
-8 8
12n_0474
4

detected by
the signature
2-3t+2t^2-t^3+t^4-t^5+2t^6-3t^7+2t^8
Seifert matrix of 12n_0474
-1 0 0 0 0 0 0 0
0 -2 0 1 1 1 1 1
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1
-1 0 -1 0 -1 -1 0 -1
-1 0 -1 0 0 -1 0 0
-1 0 -1 0 -1 -1 -1 -1
-1 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
-t^-4+2t^-3-2t^-2+2t^-1-2+2t-2t^2+2t^3-t^4
17
First homology
of the double branched cover of 12n_0474
Z/17
-8 8
12n_0475
1

detected by
an unknotting move
1-2t+t^2+t^3+t^4-2t^5+t^6
Seifert matrix of 12n_0475
1 2 0 0 2 0
1 1 0 0 2 0
0 0 -1 0 1 0
2 2 1 1 1 1
0 0 0 0 1 0
2 2 1 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,-t)
the Blanchfield form on it
-2t^-2+t^-1+2+t-2t^2
7
First homology
of the double branched cover of 12n_0475
Z/7
2 2
12n_0476
2

detected by
the signature
-3+10t-15t^2+17t^3-15t^4+10t^5-3t^6
Seifert matrix of 12n_0476
-2 -1 -1 -1 -1 -1
-1 1 -1 -1 -1 -1
-2 -1 -2 -1 -1 -1
0 0 0 -1 -1 -1
0 0 0 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(-2t,1-10t+20t^2-20t^3+24t^4-20t^5+6t^6,0,0,0,0)
the Blanchfield form on it
73
First homology
of the double branched cover of 12n_0476
Z/73
-4 4
12n_0477
3

detected by
the signature
4-8t+7t^2-5t^3+7t^4-8t^5+4t^6
Seifert matrix of 12n_0477
-1 0 0 0 0 0
0 -2 0 1 -1 1
-1 0 -1 0 0 0
-1 0 -1 -1 1 -1
1 0 1 0 -2 1
-1 0 -1 0 0 -1
1 or 2
43
First homology
of the double branched cover of 12n_0477
Z/43
-6 6
12n_0478
1

detected by
an unknotting move
2-7t+11t^2-7t^3+2t^4
Seifert matrix of 12n_0478
1 2 0 0
1 1 0 0
0 0 -1 0
2 2 1 2
1
Generator of the Alexander module
(3-2t,-3+2t,1-3t+2t^2,-1-6t+4t^2)
the Blanchfield form on it
89t^-2-494t^-1+728-494t+89t^2
29
First homology
of the double branched cover of 12n_0478
Z/29
0 0
12n_0479
1

detected by
an unknotting move
-6+21t-29t^2+21t^3-6t^4
Seifert matrix of 12n_0479
-3 -2 -2 -2
-2 0 -2 -2
-3 -2 -3 -2
-1 -1 -1 -2
1
Generator of the Alexander module
(3,2,3,1)
the Blanchfield form on it
-12t^-1+27-12t
83
First homology
of the double branched cover of 12n_0479
Z/83
-2 2
12n_0480
2

detected by
the Nakanishi index
-1+6t-19t^2+29t^3-19t^4+6t^5-t^6
Seifert matrix of 12n_0480
-2 -1 -1 1 -1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
-1 -1 0 0 0 0
-1 0 0 0 -1 -1
2
81
First homology
of the double branched cover of 12n_0480
Z/9+Z/9
0 0
12n_0481
2

detected by
the Lickorish test
-1+5t-15t^2+23t^3-15t^4+5t^5-t^6
Seifert matrix of 12n_0481
-1 0 0 0 0 0
-1 -1 0 -1 -1 0
0 0 1 0 0 0
0 0 0 1 0 0
-1 0 1 -1 -2 1
0 0 -1 1 1 0
1 or 2
65
First homology
of the double branched cover of 12n_0481
Z/65
0 0
12n_0482
1

detected by
an unknotting move
-1+6t-15t^2+21t^3-15t^4+6t^5-t^6
Seifert matrix of 12n_0482
0 -1 -1 0 0 -1
0 -1 -1 0 0 0
0 0 1 0 0 0
-1 0 0 -1 0 -2
-1 -1 0 0 0 -2
-2 -2 -2 0 -1 -5
1
Generator of the Alexander module
(0,0,0,1,0,2-t)
the Blanchfield form on it
t^-1-2+t
65
First homology
of the double branched cover of 12n_0482
Z/65
0 0
12n_0483
1

detected by
an unknotting move
-1+4t-5t^2+4t^3-t^4
Seifert matrix of 12n_0483
0 0 1 -1
0 -1 0 -1
0 0 -2 1
-1 0 2 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
1
15
First homology
of the double branched cover of 12n_0483
Z/15
-2 2
12n_0484
1

detected by
an unknotting move
1-5t+12t^2-15t^3+12t^4-5t^5+t^6
Seifert matrix of 12n_0484
-2 -1 -1 0 -1 -1
0 -1 0 0 0 0
-1 -1 0 0 0 0
-1 -1 0 -1 -1 0
-2 -1 0 0 -1 0
-1 0 -1 0 0 0
1
Generator of the Alexander module
(0,0,0,-1,0,1)
the Blanchfield form on it
-t^-1+2-t
51
First homology
of the double branched cover of 12n_0484
Z/51
-2 2
12n_0485
1

detected by
an unknotting move
2-8t+16t^2-19t^3+16t^4-8t^5+2t^6
Seifert matrix of 12n_0485
-1 0 -1 -1 0 0
0 0 0 0 -1 -1
0 -1 -1 -1 1 1
0 0 0 -1 1 1
0 -2 0 0 2 2
0 -2 0 0 1 2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-2-7t^-1+11-7t+2t^2
71
First homology
of the double branched cover of 12n_0485
Z/71
-2 2
12n_0486
2

detected by
the Lickorish test
2-7t+12t^2-13t^3+12t^4-7t^5+2t^6
Seifert matrix of 12n_0486
-1 1 -1 0 0 0
0 1 1 1 1 1
0 1 -2 -1 -1 -1
0 1 0 1 1 0
0 1 0 0 1 0
0 1 0 1 1 1
1
Generator of the Alexander module
(5-4t+2t^2-4t^3+2t^4,0,2t^2,-2-2t+2t^2,-2t+2t^2,2t^2-2t^3)
the Blanchfield form on it
t^-1+t
55
First homology
of the double branched cover of 12n_0486
Z/55
2 2
12n_0487
1

detected by
an unknotting move
-1+t+4t^2-7t^3+4t^4+t^5-t^6
Seifert matrix of 12n_0487
-1 1 -1 0 0 0
0 1 1 1 1 1
0 1 -2 -1 -1 -1
0 1 0 0 1 0
0 1 0 0 0 0
0 1 0 1 1 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
1
11
First homology
of the double branched cover of 12n_0487
Z/11
-2 2
12n_0488
1

detected by
an unknotting move
1-t-2t^2+5t^3-2t^4-t^5+t^6
Seifert matrix of 12n_0488
-1 1 -1 0 0 0
0 -3 1 -1 -1 -1
0 1 0 0 0 0
0 -1 1 0 0 -1
0 -1 1 -1 0 -1
0 -1 1 0 0 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
1
5
First homology
of the double branched cover of 12n_0488
Z/5
0 0
12n_0489
1

detected by
an unknotting move
2-11t+28t^2-37t^3+28t^4-11t^5+2t^6
Seifert matrix of 12n_0489
-1 1 -1 0 0 0
0 -3 1 -1 -1 -1
0 1 -2 -1 -1 -1
0 -1 0 -1 -1 -2
0 -1 0 -2 -1 -2
0 -1 0 -1 -1 -1
1
Generator of the Alexander module
(-2,0,0,0,1,0)
the Blanchfield form on it
4t^-2-16t^-1+27-16t+4t^2
119
First homology
of the double branched cover of 12n_0489
Z/119
-2 2
12n_0490
1

detected by
an unknotting move
5-19t+29t^2-19t^3+5t^4
Seifert matrix of 12n_0490
-1 1 -1 0
0 1 1 -1
0 1 -2 1
0 -1 0 2
1 or 2
77
First homology
of the double branched cover of 12n_0490
Z/77
0 0
12n_0491
1

detected by
an unknotting move
-1+7t-16t^2+21t^3-16t^4+7t^5-t^6
Seifert matrix of 12n_0491
-1 0 -1 -1 -1 0
0 -1 0 0 0 0
0 0 0 -1 -1 0
0 0 -1 0 0 -1
0 -1 -1 -1 0 -1
0 1 1 0 0 2
1
Generator of the Alexander module
(t-3t^2+2t^3-t^4,-t+t^2+4t^3-3t^4+t^5+3t^6-2t^7+t^8,-1+t+6t^2-5t^3-6t^4+6t^5-4t^6,5+10t+3t^2-13t^3+8t^4-12t^5-28t^6+14t^7+8t^8-38t^9+24t^10-10t^11,t-3t^2+2t^3-t^4,2+4t+2t^2-8t^3+6t^4-5t^5-15t^6+8t^7+3t^8-16t^9+10t^10-4t^11)
the Blanchfield form on it
x
69
First homology
of the double branched cover of 12n_0491
Z/69
0 2
12n_0492
1

detected by
an unknotting move
-2+9t-20t^2+27t^3-20t^4+9t^5-2t^6
Seifert matrix of 12n_0492
-2 -1 -1 0 -1 0
-1 1 -1 -1 -1 -1
-2 -1 -2 0 -1 0
1 0 1 1 0 0
0 0 0 0 -1 0
1 0 1 1 0 1
1
Generator of the Alexander module
(-2t-t^2+4t^3-4t^4,3-11t+17t^2-19t^3+12t^4-4t^5,0,3-9t+16t^2-16t^3+8t^4,-2+3t-2t^2,2t^2-3t^3+2t^4)
the Blanchfield form on it
-2819t^-5+17231t^-4-53938t^-3+111871t^-2-165725t^-1+187688-165725t+111871t^2-53938t^3+17231t^4-2819t^5
89
First homology
of the double branched cover of 12n_0492
Z/89
0 0
12n_0493
1

detected by
an unknotting move
-2+9t-21t^2+29t^3-21t^4+9t^5-2t^6
Seifert matrix of 12n_0493
-1 0 0 0 0 0
0 2 0 1 1 0
-1 0 -1 0 0 0
-1 0 -1 1 0 0
-1 0 -1 1 1 0
1 1 1 0 0 -1
1
Generator of the Alexander module
(0,1,-1,0,0,0)
the Blanchfield form on it
-2t^-2+3t^-1-1+3t-2t^2
93
First homology
of the double branched cover of 12n_0493
Z/93
0 0
12n_0494
3

detected by
the new u==2 criterion
-1+5t-8t^2+6t^3-5t^4+6t^5-8t^6+5t^7-t^8
Seifert matrix of 12n_0494
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 0 0 -1
-1 -1 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 -1 -1 -1 1 -1 -1
-1 -1 0 -1 -1 0 0 -1
2
45
First homology
of the double branched cover of 12n_0494
Z/15+Z/3
-4 4
12n_0495
2

detected by
the Nakanishi index
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 12n_0495
0 0 1 -1 -1 1
0 -1 0 0 0 0
1 -1 -2 1 1 -2
0 0 1 0 -1 1
0 0 0 0 1 0
0 -1 -1 0 0 0
2
27
First homology
of the double branched cover of 12n_0495
Z/9+Z/3
2 2
12n_0496
3

detected by
the new u==2 criterion
-1+11t-28t^2+37t^3-28t^4+11t^5-t^6
Seifert matrix of 12n_0496
-2 -1 -1 -1 0 -1
-2 -2 -1 -1 0 -1
0 0 -1 0 0 0
-1 -1 -1 -2 0 -1
0 0 0 0 -1 0
-1 -1 -1 0 1 0
2
117
First homology
of the double branched cover of 12n_0496
Z/39+Z/3
-4 4
12n_0497
2

detected by
the Lickorish test
-1+9t-25t^2+35t^3-25t^4+9t^5-t^6
Seifert matrix of 12n_0497
-1 0 0 0 0 0
0 2 0 0 0 1
-1 0 -1 0 0 0
-1 1 -1 1 -1 0
0 0 0 0 -1 -1
0 1 0 0 0 1
1 or 2
105
First homology
of the double branched cover of 12n_0497
Z/105
0 0
12n_0498
2

detected by
A(F_2)
-5+20t-29t^2+20t^3-5t^4
Seifert matrix of 12n_0498
-8 -6 -6 -5
-6 -6 -7 -4
-9 -9 -8 -6
-6 -5 -5 -4
2
79
First homology
of the double branched cover of 12n_0498
Z/79
-2 2
12n_0499
1

detected by
an unknotting move
-1+5t-10t^2+13t^3-10t^4+5t^5-t^6
Seifert matrix of 12n_0499
-1 0 -1 0 -1 0
0 1 0 -1 0 0
0 0 0 0 -1 0
0 0 0 -1 0 0
0 0 -1 -1 0 -1
0 1 1 0 0 2
1
Generator of the Alexander module
(2t-2t^2,0,4t,-2,2t,1)
the Blanchfield form on it
-1
45
First homology
of the double branched cover of 12n_0499
Z/45
0 0
12n_0500
1

detected by
an unknotting move
2-6t+11t^2-13t^3+11t^4-6t^5+2t^6
Seifert matrix of 12n_0500
0 1 0 -1 1 0
1 -2 1 1 -1 1
-1 1 0 -1 1 0
0 0 0 0 1 0
1 0 1 1 0 1
-1 1 -1 -1 1 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-2t^-2+6t^-1-9+6t-2t^2
51
First homology
of the double branched cover of 12n_0500
Z/51
2 2
12n_0501
1

detected by
an unknotting move
4-12t+17t^2-12t^3+4t^4
Seifert matrix of 12n_0501
0 0 1 -1
1 -1 0 0
1 0 1 1
-1 -1 0 0
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
2t^-2-6t^-1+8-6t+2t^2
49
First homology
of the double branched cover of 12n_0501
Z/49
0 0
12n_0502
4

detected by
the signature
2-3t+t^2+t^3-t^4+t^5+t^6-3t^7+2t^8
Seifert matrix of 12n_0502
-1 0 0 0 0 0 0 0
0 -2 0 0 0 1 0 0
-1 0 -1 0 0 0 0 0
-1 -1 -1 -1 -1 0 -1 -1
-1 -1 -1 0 -1 0 0 -1
-1 0 -1 0 0 -1 0 0
-1 -1 -1 0 -1 0 -1 -1
-1 -1 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,1,t,0,t,t,1,0)
the Blanchfield form on it
2t^-3-3t^-2+t^-1+1+t-3t^2+2t^3
9
First homology
of the double branched cover of 12n_0502
Z/9
-8 8
12n_0503
3

detected by
the signature
4-8t+5t^2-t^3+5t^4-8t^5+4t^6
Seifert matrix of 12n_0503
-1 0 0 0 0 0
0 -2 0 0 0 1
-1 0 -1 0 0 0
-1 -1 -1 -1 1 0
1 1 1 0 -2 0
-1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-3+5t^-2-4t^-1+2-4t+5t^2-2t^3
35
First homology
of the double branched cover of 12n_0503
Z/35
-6 6
12n_0504
1

detected by
an unknotting move
1-6t+15t^2-24t^3+29t^4-24t^5+15t^6-6t^7+t^8
Seifert matrix of 12n_0504
1 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 -1 0 0 -1 0
1 0 0 -1 1 -1 -1 1
0 0 0 -1 0 -1 -1 0
0 -1 0 0 0 0 -1 0
1 0 0 -1 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,2,1,0,0)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-7+4t-3t^2+t^3
121
First homology
of the double branched cover of 12n_0504
Z/121
0 0
12n_0505
2

detected by
the Nakanishi index
1-8t+24t^2-33t^3+24t^4-8t^5+t^6
Seifert matrix of 12n_0505
0 0 0 -1 -1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
-1 1 0 0 0 0
-1 0 0 -1 0 0
-1 1 0 0 0 1
2
99
First homology
of the double branched cover of 12n_0505
Z/33+Z/3
2 2
12n_0506
1

detected by
an unknotting move
1-6t+14t^2-17t^3+14t^4-6t^5+t^6
Seifert matrix of 12n_0506
-1 0 0 0 0 0
0 0 -1 0 0 0
-1 0 0 0 -1 0
0 0 -1 -1 -1 0
-1 0 -2 0 -1 -1
-1 1 0 0 -1 0
1
Generator of the Alexander module
(0,0,0,1,0,1)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
59
First homology
of the double branched cover of 12n_0506
Z/59
-2 2
12n_0507
1

detected by
an unknotting move
1-7t+18t^2-23t^3+18t^4-7t^5+t^6
Seifert matrix of 12n_0507
1 0 1 0 1 1
0 0 -1 0 0 0
0 0 2 0 1 1
0 0 1 -1 1 0
0 0 0 0 1 0
0 1 2 0 1 1
1
Generator of the Alexander module
(1,0,0,3-t,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
75
First homology
of the double branched cover of 12n_0507
Z/75
2 2
12n_0508
2

detected by
the Nakanishi index
-1+4t-10t^2+16t^3-19t^4+16t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0508
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 1 0 -1 0
0 0 0 -1 0 0 -1 0
0 0 0 -1 1 0 -1 0
-1 -1 0 0 0 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 1 0 -1 1 -1
2
81
First homology
of the double branched cover of 12n_0508
Z/27+Z/3
-4 4
12n_0509
2

detected by
the Nakanishi index
1-5t+8t^2-7t^3+7t^4-7t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0509
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
-1 -1 0 -1 -1 0 0 0
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 0 1 0
-1 0 0 0 -1 0 1 -1
2
49
First homology
of the double branched cover of 12n_0509
Z/7+Z/7
-4 4
12n_0510
2

detected by
the Nakanishi index
-1+11t-29t^2+39t^3-29t^4+11t^5-t^6
Seifert matrix of 12n_0510
0 -1 -1 -1 0 0
0 1 -1 1 1 0
0 0 1 0 0 0
0 0 -1 1 1 0
1 2 0 2 2 -1
0 0 0 0 0 1
2
121
First homology
of the double branched cover of 12n_0510
Z/11+Z/11
4 4
12n_0511
1

detected by
an unknotting move
-2+9t-19t^2+25t^3-19t^4+9t^5-2t^6
Seifert matrix of 12n_0511
0 0 1 0 1 -1
0 -1 0 0 0 0
0 -1 -1 -2 -1 0
-1 -1 -2 -1 -2 1
0 -1 -1 -1 0 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-1-2+t
85
First homology
of the double branched cover of 12n_0511
Z/85
0 0
12n_0512
1

detected by
an unknotting move
2-7t+15t^2-19t^3+15t^4-7t^5+2t^6
Seifert matrix of 12n_0512
-1 0 -1 1 -1 0
0 1 0 0 0 0
0 0 0 1 -1 0
0 1 1 1 1 1
0 0 -1 0 0 -1
0 1 1 1 0 2
1
Generator of the Alexander module
(-1-t+t^2,0,-3t+t^3,2+2t-t^3,0,0)
the Blanchfield form on it
-2t^-2+3t^-1-6+3t-2t^2
67
First homology
of the double branched cover of 12n_0512
Z/67
2 2
12n_0513
2

detected by
the signature
-2+13t-29t^2+37t^3-29t^4+13t^5-2t^6
Seifert matrix of 12n_0513
-1 0 -1 1 -1 0
0 -1 0 -1 0 -1
0 0 -2 1 -1 -1
0 0 1 -1 2 -1
0 0 -1 1 -2 0
0 0 0 -1 1 -2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
125
First homology
of the double branched cover of 12n_0513
Z/125
-4 4
12n_0514
1

detected by
an unknotting move
1-3t+8t^2-11t^3+8t^4-3t^5+t^6
Seifert matrix of 12n_0514
-1 1 -1 0 -1 0
0 1 1 1 1 1
0 1 0 0 -1 0
0 1 1 2 1 1
0 1 0 0 0 0
0 1 1 2 1 2
1
Generator of the Alexander module
(2t-3t^2+2t^3-t^4-t^5+t^6,0,-1+3t-2t^2-t^3+t^4,-2+t^2-t^3+2t^4-t^5,t-3t^2+2t^3+t^4-t^5,1-2t-t^2+3t^3-t^5)
the Blanchfield form on it
x
35
First homology
of the double branched cover of 12n_0514
Z/35
2 2
12n_0515
2

detected by
the signature
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 12n_0515
-1 1 -1 0 -1 0
0 -3 1 -1 1 -1
0 1 -1 -1 -2 -1
0 -1 0 -2 0 -2
0 1 -1 -1 -1 -1
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(27-120t+170t^2-123t^3+48t^4-12t^5+4t^6,8-71t+131t^2-146t^3+94t^4-28t^5-8t^6+8t^7,11+130t-235t^2+168t^3-52t^4-4t^5,-74+121t-80t^2+20t^3+4t^4,4-40t+59t^2-36t^3+4t^4+4t^5,166-274t+184t^2-48t^3-8t^4)
the Blanchfield form on it
x
89
First homology
of the double branched cover of 12n_0515
Z/89
-4 4
12n_0516
2

detected by
the signature
-2+11t-22t^2+27t^3-22t^4+11t^5-2t^6
Seifert matrix of 12n_0516
-1 1 -1 0 -1 0
0 -3 1 -1 1 -1
0 1 -2 -1 -2 -1
0 -1 0 -1 0 -2
0 1 -1 -1 -2 -1
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(-2+3t-16t^2+11t^3-2t^4,0,1+6t^2-2t^3,-12+7t+2t^2-t^3,1+6t^2-2t^3,-3+t)
the Blanchfield form on it
1507t^-3-8326t^-2+16805t^-1-20648+16805t-8326t^2+1507t^3
97
First homology
of the double branched cover of 12n_0516
Z/97
-4 4
12n_0517
1

detected by
an unknotting move
-1+4t-11t^2+21t^3-27t^4+21t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0517
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 1 1 0 1 0
-1 -1 0 0 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 0 1 0 1 1
1
Generator of the Alexander module
(0,-1-t+4t^2-7t^3+7t^4+15t^5-45t^6+54t^7-36t^8+13t^9-2t^10,3t^2-3t^3-5t^4+32t^5-59t^6+60t^7-37t^8+13t^9-2t^10,-2t-t^2+11t^3-17t^4+14t^5-6t^6+t^7,-3t+15t^2-7t^3-52t^4+187t^5-296t^6+277t^7-161t^8+54t^9-8t^10,6t^2-6t^3-10t^4+64t^5-118t^6+120t^7-74t^8+26t^9-4t^10,-3t+3t^2+5t^3-32t^4+59t^5-60t^6+37t^7-13
the Blanchfield form on it
x
101
First homology
of the double branched cover of 12n_0517
Z/101
0 0
12n_0518
3

detected by
the signature
-1+6t^2-16t^3+21t^4-16t^5+6t^6-t^8
Seifert matrix of 12n_0518
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 1 0
0 0 -1 -1 0 0 0 0
-1 -1 0 0 -1 0 1 0
0 0 0 0 -1 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
63
First homology
of the double branched cover of 12n_0518
Z/21+Z/3
-6 6
12n_0519
1

detected by
an unknotting move
2-3t+2t^2
Seifert matrix of 12n_0519
7 3
4 2
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
-1
7
First homology
of the double branched cover of 12n_0519
Z/7
2 2
12n_0520
1

detected by
an unknotting move
-4+18t-27t^2+18t^3-4t^4
Seifert matrix of 12n_0520
14 -3 2 -5
-4 3 0 2
-1 2 2 1
-5 2 0 2
1
Generator of the Alexander module
(1,0,1,0)
the Blanchfield form on it
-2t^-2+9t^-1-14+9t-2t^2
71
First homology
of the double branched cover of 12n_0520
Z/71
2 2
12n_0521
1

detected by
an unknotting move
1-6t+14t^2-18t^3+17t^4-18t^5+14t^6-6t^7+t^8
Seifert matrix of 12n_0521
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
0 0 1 0 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 -1 -1 0 -1 0
-1 0 0 -1 -1 -1 0 0
0 0 1 0 0 0 1 0
0 0 -1 -1 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,-1+t+9t^2+18t^3+5t^4-6t^5+6t^6,1+t+7t^2+15t^3+18t^4+5t^5-6t^6+6t^7,-1+t+4t^2+11t^3+14t^4-8t^5-6t^6+12t^7,-4t-5t^2-8t^3+5t^4+26t^5+24t^6+11t^7-6t^8+6t^9,0,-1-t+11t^2+36t^3+41t^4+4t^5-6t^6+12t^7)
the Blanchfield form on it
x
95
First homology
of the double branched cover of 12n_0521
Z/95
-2 2
12n_0522
1

detected by
an unknotting move
1-2t+5t^2-7t^3+5t^4-2t^5+t^6
Seifert matrix of 12n_0522
-1 1 -1 -1 -1 -1
0 1 1 1 1 1
0 1 0 -1 -1 -1
0 1 0 0 0 -1
0 1 0 -1 0 -1
0 1 0 0 0 0
1
Generator of the Alexander module
(1,0,0,1,0,0)
the Blanchfield form on it
t^-1-2+t
23
First homology
of the double branched cover of 12n_0522
Z/23
2 2
12n_0523
1

detected by
an unknotting move
2-3t+3t^2-3t^3+2t^4
Seifert matrix of 12n_0523
-1 1 -1 1
0 1 1 -1
0 1 0 1
0 -1 0 1
1
Generator of the Alexander module
(t^2-7t^3+3t^4-4t^5+4t^6,-2t-13t^2+33t^3-19t^4+20t^5-20t^6,11t^2-6t^3+4t^4-8t^5,1+6t-24t^2+14t^3-12t^4+16t^5)
the Blanchfield form on it
5867t^-3-14713t^-2+24009t^-1-27446+24009t-14713t^2+5867t^3
13
First homology
of the double branched cover of 12n_0523
Z/13
0 2
12n_0524
1

detected by
an unknotting move
2-11t+21t^2-23t^3+21t^4-11t^5+2t^6
Seifert matrix of 12n_0524
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 0 0 0
0 0 1 -1 -1 0
-1 1 1 0 -1 0
0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-2-13t^-1+23-13t+2t^2
91
First homology
of the double branched cover of 12n_0524
Z/91
-2 2
12n_0525
1

detected by
an unknotting move
-1+8t-28t^2+43t^3-28t^4+8t^5-t^6
Seifert matrix of 12n_0525
-1 0 0 0 1 1
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 -1 0 0 1 0
0 -1 -1 1 0 -1
1 or 2
117
First homology
of the double branched cover of 12n_0525
Z/117
0 0
12n_0526
2

detected by
the signature
1-4t+6t^2-3t^3+t^4-3t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0526
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 1 0 0 1 0 0 0
0 1 0 0 1 -1 -1 -1
-1 0 -1 0 0 0 -1 0
-1 0 -1 0 0 0 -1 -1
2
29
First homology
of the double branched cover of 12n_0526
Z/29
-4 4
12n_0527
2

detected by
the signature
-3+12t-20t^2+23t^3-20t^4+12t^5-3t^6
Seifert matrix of 12n_0527
1 0 0 0 0 0
-1 -1 1 -1 -1 1
0 0 -2 1 0 -1
0 0 0 -1 0 0
-1 0 0 -1 -1 1
0 0 -1 1 0 -2
1
Generator of the Alexander module
(0,-5+28t-45t^2+18t^3,5-13t+6t^2+10t^3-6t^4,-5+3t,-7+21t-19t^2-4t^3-4t^4+6t^5,-5t-2t^2+3t^3)
the Blanchfield form on it
9739t^-3-38956t^-2+64927t^-1-74666+64927t-38956t^2+9739t^3
93
First homology
of the double branched cover of 12n_0527
Z/93
-4 4
12n_0528
2

detected by
the signature
1+2t-10t^2+15t^3-10t^4+2t^5+t^6
Seifert matrix of 12n_0528
1 0 0 0 0 0
0 1 0 0 1 0
0 0 1 0 0 0
1 0 0 1 0 0
1 0 1 -1 1 0
1 0 1 0 0 1
1 or 2
37
First homology
of the double branched cover of 12n_0528
Z/37
4 4
12n_0529
1

detected by
an unknotting move
1-10t+28t^2-37t^3+28t^4-10t^5+t^6
Seifert matrix of 12n_0529
1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
1 0 0 -2 0 -1
1 -1 1 -1 -1 0
1 0 1 -1 0 -1
1 or 2
115
First homology
of the double branched cover of 12n_0529
Z/115
-2 2
12n_0530
1

detected by
an unknotting move
2-10t+19t^2-21t^3+19t^4-10t^5+2t^6
Seifert matrix of 12n_0530
0 1 1 0 1 0
0 -1 0 0 0 0
1 0 0 0 -1 0
1 0 -2 -2 -2 1
1 -1 -2 0 -1 0
-1 0 1 1 1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-2t^-2+5t^-1-4+5t-2t^2
83
First homology
of the double branched cover of 12n_0530
Z/83
-2 2
12n_0531
1

detected by
an unknotting move
-1+4t-11t^2+20t^3-25t^4+20t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0531
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 1 1 0 1 0
-1 -1 0 0 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 1 1 0 1 1
1
Generator of the Alexander module
(0,0,1,1,1,-t,1,-t)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-14+11t-5t^2+t^3
97
First homology
of the double branched cover of 12n_0531
Z/97
0 0
12n_0532
1

detected by
an unknotting move
-2+11t-29t^2+41t^3-29t^4+11t^5-2t^6
Seifert matrix of 12n_0532
-1 -1 0 0 0 0
0 -1 0 0 0 0
1 1 2 0 1 0
1 1 0 0 0 -1
1 0 0 0 1 0
1 1 1 -1 1 -1
1
Generator of the Alexander module
(0,0,3-2t,0,0,1-2t)
the Blanchfield form on it
-t^-2+3t^-1-6+3t-t^2
125
First homology
of the double branched cover of 12n_0532
Z/125
0 0
12n_0533
2

detected by
the Lickorish test
-1+4t-8t^2+12t^3-13t^4+12t^5-8t^6+4t^7-t^8
Seifert matrix of 12n_0533
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 1 0 0 1 1 0 0
0 0 0 0 0 1 0 0
-1 0 -1 0 0 0 -1 0
0 1 0 0 1 0 -1 -1
2
63
First homology
of the double branched cover of 12n_0533
Z/63
-2 2
12n_0534
1

detected by
an unknotting move
-2+11t-25t^2+33t^3-25t^4+11t^5-2t^6
Seifert matrix of 12n_0534
-1 0 0 -1 1 0
0 2 0 0 0 0
0 1 -1 0 0 0
0 -1 -1 -1 0 -1
0 1 0 0 1 1
0 1 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
109
First homology
of the double branched cover of 12n_0534
Z/109
0 0
12n_0535
1

detected by
an unknotting move
-1+7t-11t^2+7t^3-t^4
Seifert matrix of 12n_0535
11 3 8 6
3 2 2 2
11 3 7 6
5 2 4 3
1
Generator of the Alexander module
(1-t+12t^2+225t^3-228t^4+36t^5,20-20t-245t^2+426t^3-777t^4+138t^5,41-41t-533t^2+615t^3-1353t^4+246t^5,-24+24t+307t^2-402t^3+831t^4-150t^5)
the Blanchfield form on it
-119561t^-1-749750-119561t
27
First homology
of the double branched cover of 12n_0535
Z/27
2 2
12n_0536
1

detected by
an unknotting move
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 12n_0536
-1 0 -1 1 -1 -1
0 -1 0 0 1 1
0 0 1 0 0 0
0 0 0 1 0 0
0 0 -1 0 0 1
0 0 -1 -1 1 2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-t^-1+3-t
81
First homology
of the double branched cover of 12n_0536
Z/81
0 0
12n_0537
1

detected by
an unknotting move
2-12t+27t^2-33t^3+27t^4-12t^5+2t^6
Seifert matrix of 12n_0537
0 1 1 0 0 -1
0 -1 0 0 0 0
0 -1 -1 0 0 0
0 0 0 -1 0 -1
0 -1 0 0 2 2
-1 0 0 0 1 0
1
Generator of the Alexander module
(2,0,0,2,-1-2t,0)
the Blanchfield form on it
5t^-3-30t^-2+67t^-1-82+67t-30t^2+5t^3
115
First homology
of the double branched cover of 12n_0537
Z/115
-2 2
12n_0538
2

detected by
the signature
1-5t+10t^2-11t^3+11t^4-11t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0538
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 1 0 0 1 0 0 0
0 1 0 0 1 -1 -1 -1
-1 0 -1 0 0 0 -1 0
0 0 0 0 1 0 -1 -1
1 or 2
65
First homology
of the double branched cover of 12n_0538
Z/65
-4 4
12n_0539
1

detected by
an unknotting move
-1+5t-14t^2+27t^3-33t^4+27t^5-14t^6+5t^7-t^8
Seifert matrix of 12n_0539
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 1 0 0 1 1 0 0
-1 0 -1 0 0 1 1 1
0 0 0 0 1 1 0 1
1
Generator of the Alexander module
(0,0,t,1+t,0,0,1+t,0)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+11-8t+4t^2-t^3
127
First homology
of the double branched cover of 12n_0539
Z/127
-2 2
12n_0540
2

detected by
the Lickorish test
2-10t+21t^2-25t^3+21t^4-10t^5+2t^6
Seifert matrix of 12n_0540
-1 -1 0 0 -1 1
0 -1 0 0 -1 1
0 0 2 0 0 0
0 0 1 -1 0 0
0 0 -1 -1 -1 0
0 0 1 0 0 1
1
Generator of the Alexander module
(-1+t,0,0,0,-1,1)
the Blanchfield form on it
2t^-2-8t^-1+13-8t+2t^2
91
First homology
of the double branched cover of 12n_0540
Z/91
-2 2
12n_0541
1

detected by
an unknotting move
2-9t+19t^2-23t^3+19t^4-9t^5+2t^6
Seifert matrix of 12n_0541
1 0 0 0 0 0
1 1 0 1 0 1
1 1 2 1 0 1
1 1 1 0 0 1
0 1 0 0 -1 1
1 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,-t,t)
the Blanchfield form on it
2t^-2-5t^-1+6-5t+2t^2
83
First homology
of the double branched cover of 12n_0541
Z/83
2 2
12n_0542
1

detected by
an unknotting move
1-9t+28t^2-39t^3+28t^4-9t^5+t^6
Seifert matrix of 12n_0542
1 0 0 0 0 0
-1 -1 -1 1 -1 1
0 0 1 0 0 0
1 0 0 1 0 0
-1 0 -1 1 -1 1
1 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-2-5t^-1+7-5t+t^2
115
First homology
of the double branched cover of 12n_0542
Z/115
2 2
12n_0543
2

detected by
the Lickorish test
1-5t+15t^2-21t^3+15t^4-5t^5+t^6
Seifert matrix of 12n_0543
-1 1 -1 0 0 -1
0 1 1 1 0 1
0 1 0 0 1 -1
0 1 1 2 1 1
0 0 0 0 1 0
0 1 0 0 1 0
1 or 2
63
First homology
of the double branched cover of 12n_0543
Z/63
2 2
12n_0544
1

detected by
an unknotting move
2-12t+28t^2-35t^3+28t^4-12t^5+2t^6
Seifert matrix of 12n_0544
-1 1 -1 0 0 -1
0 1 1 1 0 1
0 1 -2 -1 0 -2
0 1 0 1 0 0
0 0 -1 -1 -1 -1
0 1 -1 -1 0 -2
1
Generator of the Alexander module
(0,0,1,1,-t,1)
the Blanchfield form on it
-2t^-1+5-2t
119
First homology
of the double branched cover of 12n_0544
Z/119
-2 2
12n_0545
2

detected by
the signature
-2+10t-19t^2+23t^3-19t^4+10t^5-2t^6
Seifert matrix of 12n_0545
-1 1 -1 0 0 -1
0 -3 1 -1 0 1
0 1 -1 -1 0 -2
0 -1 0 -2 0 0
0 0 -1 -1 -1 -1
0 1 -1 -1 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
85
First homology
of the double branched cover of 12n_0545
Z/85
-4 4
12n_0546
2

detected by
the Nakanishi index
2-8t+14t^2-15t^3+14t^4-8t^5+2t^6
Seifert matrix of 12n_0546
1 1 1 1 0 1
0 1 0 1 0 0
0 1 2 1 0 0
0 1 1 0 0 0
0 0 -1 -1 -1 0
0 1 1 1 0 1
2
63
First homology
of the double branched cover of 12n_0546
Z/21+Z/3
2 2
12n_0547
1

detected by
an unknotting move
4-17t+27t^2-17t^3+4t^4
Seifert matrix of 12n_0547
-1 0 -1 -1
0 2 1 2
0 2 3 2
0 2 2 1
1
Generator of the Alexander module
(2-t,1,0,0)
the Blanchfield form on it
1
69
First homology
of the double branched cover of 12n_0547
Z/69
0 0
12n_0548
1

detected by
an unknotting move
-1+8t-20t^2+27t^3-20t^4+8t^5-t^6
Seifert matrix of 12n_0548
0 0 -1 1 -1 0
1 -1 0 1 0 -1
-1 -1 0 0 0 0
0 0 0 1 0 0
-1 0 -1 0 0 0
1 0 0 1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+2t^-1-3+2t-t^2
85
First homology
of the double branched cover of 12n_0548
Z/85
0 0
12n_0549
2

detected by
the Nakanishi index
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 12n_0549
-1 0 0 0 0 -1
0 -1 0 -1 0 -1
0 0 0 0 0 -1
0 0 0 -1 -1 -1
0 0 -1 0 0 -1
0 0 -1 0 -1 -3
2
27
First homology
of the double branched cover of 12n_0549
Z/9+Z/3
-2 2
12n_0550
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 12n_0550
1 0 0 0
-2 -2 -2 -2
-1 -2 0 -1
-1 -1 0 -1
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
t^-1-2+t
33
First homology
of the double branched cover of 12n_0550
Z/33
0 0
12n_0551
2

detected by
the signature
-3+13t-23t^2+27t^3-23t^4+13t^5-3t^6
Seifert matrix of 12n_0551
1 0 0 0 0 0
-1 -1 1 0 1 0
1 0 -2 0 -1 -1
0 0 0 -1 0 -1
1 0 -1 -1 -2 -1
0 0 0 0 0 -1
1 or 2
105
First homology
of the double branched cover of 12n_0551
Z/105
-4 4
12n_0552
1

detected by
an unknotting move
-1+3t-t^2-t^3-t^4+3t^5-t^6
Seifert matrix of 12n_0552
1 0 0 0 0 0
-1 -1 1 0 1 0
1 0 0 -1 -1 -1
0 0 0 -1 0 -1
1 0 -1 -1 0 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,1,0,0)
the Blanchfield form on it
t^-1-2+t
9
First homology
of the double branched cover of 12n_0552
Z/9
0 2
12n_0553
3

detected by
the Nakanishi index
4-20t+33t^2-20t^3+4t^4
Seifert matrix of 12n_0553
-3 -4 0 -2
-5 -4 1 -2
0 0 -1 0
-1 -1 0 0
3
81
First homology
of the double branched cover of 12n_0553
Z/3+Z/9+Z/3
0 0
12n_0554
3

detected by
the Nakanishi index
-2+7t-9t^2+7t^3-2t^4
Seifert matrix of 12n_0554
-3 -4 0 -2
-5 -5 1 -2
0 0 1 0
-1 -1 0 0
3
27
First homology
of the double branched cover of 12n_0554
Z/3+Z/3+Z/3
2 2
12n_0555
3

detected by
the Nakanishi index
1-9t+33t^2-49t^3+33t^4-9t^5+t^6
Seifert matrix of 12n_0555
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
1 0 0 1 1 1
-1 -1 0 0 -1 -1
-1 0 -1 0 0 -1
3
135
First homology
of the double branched cover of 12n_0555
Z/15+Z/3+Z/3
2 2
12n_0556
3

detected by
the Nakanishi index
4-20t+33t^2-20t^3+4t^4
Seifert matrix of 12n_0556
1 0 0 0
1 1 -1 0
1 0 -2 0
1 -1 -1 -2
2
81
First homology
of the double branched cover of 12n_0556
Z/9+Z/3+Z/3
0 0
12n_0557
2

detected by
the signature
-3+12t-21t^2+25t^3-21t^4+12t^5-3t^6
Seifert matrix of 12n_0557
-1 -1 0 0 -1 0
0 -2 0 0 -1 0
0 1 -1 0 1 0
0 0 0 1 -1 0
0 -1 0 0 -2 0
0 0 -1 0 1 -1
1
Generator of the Alexander module
(-2+13t-7t^2-43t^3+46t^4+48t^5-76t^6+24t^7,-4-10t+34t^2-102t^3+92t^4+96t^5-152t^6+48t^7,7-24t+36t^2+28t^3-138t^4+108t^5+96t^6-152t^7+48t^8,-2+22t-19t^2-39t^3+46t^4+48t^5-76t^6+24t^7,-1-49t+48t^2+23t^3-156t^4+174t^5+64t^6-272t^7+200t^8-48t^9,-t+2t^2-30t^3+24t^4+82t^5-92t^6-96t^7+152t^8-48t^9)
the Blanchfield form on it
x
97
First homology
of the double branched cover of 12n_0557
Z/97
-4 4
12n_0558
2

detected by
the Lickorish test
1-3t+8t^2-11t^3+8t^4-3t^5+t^6
Seifert matrix of 12n_0558
-1 0 -1 0 0 0
0 -1 1 1 -1 1
0 0 -1 1 -1 1
0 0 0 1 0 1
0 0 0 0 -1 0
0 0 0 0 0 1
1 or 2
35
First homology
of the double branched cover of 12n_0558
Z/35
-2 2
12n_0559
2

detected by
the signature
-2+7t-11t^2+13t^3-11t^4+7t^5-2t^6
Seifert matrix of 12n_0559
-1 0 0 0 2 1
0 0 0 0 1 0
0 0 -1 -1 -2 -1
0 -1 0 -1 0 0
0 0 0 -2 -6 -4
0 -1 0 -1 -2 -1
1
Generator of the Alexander module
(0,0,1,2,0,2)
the Blanchfield form on it
t^-1-1+t
53
First homology
of the double branched cover of 12n_0559
Z/53
-4 4
12n_0560
1

detected by
an unknotting move
-3+14t-30t^2+39t^3-30t^4+14t^5-3t^6
Seifert matrix of 12n_0560
-1 -1 -1 -1 0 0
0 -1 -1 -1 -1 0
0 -2 -1 -1 -1 0
0 -2 -2 0 -1 0
0 0 0 -1 1 0
0 -1 -1 0 -1 -1
1
Generator of the Alexander module
(-t^2+t^3,0,0,1+t^2,0,t)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
133
First homology
of the double branched cover of 12n_0560
Z/133
0 0
12n_0561
2

detected by
the Lickorish test
-4+14t-19t^2+14t^3-4t^4
Seifert matrix of 12n_0561
-1 0 -1 0
0 -1 -1 -1
0 -1 -2 0
0 0 0 4
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
-4t^-1+9-4t
55
First homology
of the double branched cover of 12n_0561
Z/55
-2 2
12n_0562
2

detected by
the Lickorish test
-3+9t-11t^2+9t^3-3t^4
Seifert matrix of 12n_0562
-3 -5 -6 0
-6 -9 -9 0
-5 -6 -6 1
-1 -2 -1 -1
1 or 2
35
First homology
of the double branched cover of 12n_0562
Z/35
-2 2
12n_0563
1

detected by
an unknotting move
-5+18t-25t^2+18t^3-5t^4
Seifert matrix of 12n_0563
-4 -9 -10 -8
-10 -25 -25 -20
-9 -20 -20 -17
-7 -16 -17 -14
1
Generator of the Alexander module
(0,-22+40t-16t^2,-14+22t-8t^2,3-2t)
the Blanchfield form on it
1192t^-4-10696t^-3+40299t^-2-83934t^-1+106278-83934t+40299t^2-10696t^3+1192t^4
71
First homology
of the double branched cover of 12n_0563
Z/71
-2 2
12n_0564
1

detected by
an unknotting move
-2+10t-15t^2+10t^3-2t^4
Seifert matrix of 12n_0564
-3 0 -2 -2
0 1 0 0
-1 0 0 -1
0 1 0 1
1
Generator of the Alexander module
(-4+6t-2t^2,0,1,0)
the Blanchfield form on it
t^-1-2+t
39
First homology
of the double branched cover of 12n_0564
Z/39
2 2
12n_0565
2

detected by
the Nakanishi index
-2+7t-9t^2+9t^3-9t^4+7t^5-2t^6
Seifert matrix of 12n_0565
1 0 0 0 0 0
0 1 0 0 0 0
0 1 1 0 1 0
1 0 0 -2 0 -1
0 1 0 0 1 0
1 1 1 0 1 1
2
45
First homology
of the double branched cover of 12n_0565
Z/15+Z/3
4 4
12n_0566
1

detected by
an unknotting move
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 12n_0566
1 0 0 0
1 -2 0 -1
0 0 2 1
1 0 0 1
1 or 2
63
First homology
of the double branched cover of 12n_0566
Z/63
2 2
12n_0567
2

detected by
the Nakanishi index
-3+13t-26t^2+33t^3-26t^4+13t^5-3t^6
Seifert matrix of 12n_0567
-4 -2 -5 0 -7 -4
-3 -1 -3 0 -4 -2
-4 -2 -4 0 -7 -4
-2 -1 -1 -1 -2 -1
-6 -3 -6 0 -9 -6
-3 -1 -3 0 -5 -3
2
117
First homology
of the double branched cover of 12n_0567
Z/39+Z/3
0 0
12n_0568
1

detected by
an unknotting move
3-12t+24t^2-29t^3+24t^4-12t^5+3t^6
Seifert matrix of 12n_0568
-4 -2 0 0 -7 -4
-3 -1 0 0 -4 -2
-2 -1 -1 0 -2 -1
-1 -1 -1 -1 -2 -1
-6 -3 0 0 -9 -6
-3 -1 0 0 -5 -3
1
Generator of the Alexander module
(0,0,1-t-5t^2+t^3+3t^5-t^6,-1+3t^2-t^5,1+2t-t^4,0)
the Blanchfield form on it
107
First homology
of the double branched cover of 12n_0568
Z/107
-2 2
12n_0569
1

detected by
an unknotting move
3-10t+18t^2-21t^3+18t^4-10t^5+3t^6
Seifert matrix of 12n_0569
-9 -3 -6 3 -10 -6
-4 -1 -3 1 -4 -3
-7 -2 -4 2 -7 -4
1 0 0 -1 1 0
-9 -3 -6 3 -9 -6
-7 -2 -5 2 -7 -4
1
Generator of the Alexander module
(0,-1+t+t^2,0,0,0,2+t)
the Blanchfield form on it
-4t^-4+43t^-3-126t^-2+218t^-1-254+218t-126t^2+43t^3-4t^4
83
First homology
of the double branched cover of 12n_0569
Z/83
2 2
12n_0570
2

detected by
the Nakanishi index
1-3t+6t^2-8t^3+9t^4-8t^5+6t^6-3t^7+t^8
Seifert matrix of 12n_0570
-1 0 0 -1 -1 0 0 -1
0 1 0 0 0 1 0 0
0 1 1 0 0 1 1 0
0 0 0 0 -1 0 0 -1
0 1 1 -1 0 1 1 -1
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
0 0 0 0 -1 0 0 0
2
45
First homology
of the double branched cover of 12n_0570
Z/15+Z/3
4 4
12n_0571
2

detected by
the Nakanishi index
-1+3t-4t^2+4t^3-3t^4+4t^5-4t^6+3t^7-t^8
Seifert matrix of 12n_0571
-1 0 0 -1 -1 0 0 -1
0 1 0 0 0 1 0 0
0 1 1 0 0 1 1 0
0 0 0 -2 -1 0 0 -2
0 1 1 -1 0 1 1 -1
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
0 0 0 -1 -1 0 0 -2
2
27
First homology
of the double branched cover of 12n_0571
Z/9+Z/3
2 2
12n_0572
1

detected by
an unknotting move
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 12n_0572
-1 0 0 -1 -1 -1
0 2 0 0 0 0
0 -1 1 0 0 0
0 0 0 0 -1 -1
0 -1 1 -1 0 -1
0 0 0 0 -1 0
1
Generator of the Alexander module
(1-2t,0,-1,0,0,1)
the Blanchfield form on it
4t^-2-10t^-1+13-10t+4t^2
63
First homology
of the double branched cover of 12n_0572
Z/63
2 2
12n_0573
1

detected by
an unknotting move
-2+7t-12t^2+15t^3-12t^4+7t^5-2t^6
Seifert matrix of 12n_0573
-1 0 0 -1 -1 -1
0 2 0 0 0 0
0 -1 1 0 0 0
0 0 0 -2 -1 -2
0 -1 1 -1 0 -1
0 0 0 -1 -1 -2
1
Generator of the Alexander module
(t,0,1,0,0,0)
the Blanchfield form on it
-t^-1+2-t
57
First homology
of the double branched cover of 12n_0573
Z/57
0 2
12n_0574
4

detected by
the signature
-1+t-2t^3+3t^4-3t^5+3t^6-2t^7+t^9-t^10
Seifert matrix of 12n_0574
-1 0 0 0 0 0 0 0 0 0
0 -1 -1 0 -1 -1 0 -1 -1 -1
0 0 -1 0 -1 -1 0 0 -1 -1
-1 0 0 -1 0 0 0 0 0 0
-1 0 0 -1 -1 -1 0 0 0 -1
-1 0 0 -1 0 -1 0 0 0 0
0 -1 -1 0 -1 -1 -1 -1 -1 -1
0 0 -1 0 -1 -1 0 -1 -1 -1
0 0 0 0 -1 -1 0 0 -1 -1
-1 0 0 -1 0 -1 0 0 0 -1
2
9
First homology
of the double branched cover of 12n_0574
Z/3+Z/3
-8 8
12n_0575
3

detected by
the signature
2-3t+t^2+4t^3-7t^4+4t^5+t^6-3t^7+2t^8
Seifert matrix of 12n_0575
-1 0 0 0 0 0 0 0
0 -1 1 0 -1 -1 0 -1
0 0 -2 0 1 1 0 1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 -1 1 0 -1 -1 -1 -1
-1 0 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,1+2t,-t,-t,0,0,1+t,0)
the Blanchfield form on it
4t^-3-3t^-2-4t^-1+8-4t-3t^2+4t^3
3
First homology
of the double branched cover of 12n_0575
Z/3
-6 6
12n_0576
4

detected by
the signature
2-4t+5t^2-4t^3+3t^4-4t^5+5t^6-4t^7+2t^8
Seifert matrix of 12n_0576
-1 0 0 0 0 0 0 0
0 -2 -2 0 1 1 -2 1
0 -1 -2 0 1 1 -1 1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 -1 -2 0 1 1 -2 1
-1 0 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1+t+t^3-2t^4,t,0,0,0,0)
the Blanchfield form on it
10t^-3-14t^-2+7t^-1-2+7t-14t^2+10t^3
33
First homology
of the double branched cover of 12n_0576
Z/33
-8 8
12n_0577
1

detected by
an unknotting move
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 12n_0577
1 0 2 0 2 0
-1 -3 -1 -2 1 -3
1 0 1 0 2 0
0 -1 0 -1 1 -1
0 0 0 0 1 0
-1 -2 -1 -2 1 -3
1
Generator of the Alexander module
(0,0,0,t,0,1+2t)
the Blanchfield form on it
3t^-2-8t^-1+12-8t+3t^2
27
First homology
of the double branched cover of 12n_0577
Z/27
-2 2
12n_0578
1

detected by
an unknotting move
-3+11t-20t^2+25t^3-20t^4+11t^5-3t^6
Seifert matrix of 12n_0578
-2 -1 -1 -1 -1 -1
-1 1 0 -1 -1 0
-1 1 1 -1 -1 1
-2 -1 -1 -2 -1 -1
0 0 0 0 -1 0
-1 1 0 -1 -1 1
1
Generator of the Alexander module
(1,0,0,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
93
First homology
of the double branched cover of 12n_0578
Z/93
0 2
12n_0579
1

detected by
an unknotting move
1-2t-3t^2+9t^3-3t^4-2t^5+t^6
Seifert matrix of 12n_0579
1 0 0 0 0 0
1 0 1 -1 0 0
0 0 1 0 0 0
1 -1 0 -2 -1 -1
1 -1 1 -1 0 0
1 0 1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,-t,t)
the Blanchfield form on it
1
9
First homology
of the double branched cover of 12n_0579
Z/9
0 0
12n_0580
2

detected by
the Lickorish test
5-16t+23t^2-16t^3+5t^4
Seifert matrix of 12n_0580
0 -1 6 3
0 -1 1 1
5 0 30 15
2 0 14 7
1 or 2
65
First homology
of the double branched cover of 12n_0580
Z/65
0 0
12n_0581
3

detected by
the signature
3-5t+4t^2-3t^3+4t^4-5t^5+3t^6
Seifert matrix of 12n_0581
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 -1
-1 -1 0 -1 0 0
0 0 -1 -1 -3 -1
-1 -1 0 -1 0 -1
2
27
First homology
of the double branched cover of 12n_0581
Z/9+Z/3
-6 6
12n_0582
2

detected by
the Nakanishi index
1-2t+3t^2-2t^3+t^4
Seifert matrix of 12n_0582
-4 -3 -3 -3
-4 -4 -3 -3
-3 -3 -2 -3
-3 -3 -2 -2
2
9
First homology
of the double branched cover of 12n_0582
Z/3+Z/3
0 0
12n_0583
2

detected by
the Nakanishi index
-5+16t-21t^2+16t^3-5t^4
Seifert matrix of 12n_0583
-2 -1 -1 -1
-2 -2 -1 -1
0 0 -1 0
-1 -1 -1 2
2
63
First homology
of the double branched cover of 12n_0583
Z/21+Z/3
-2 2
12n_0584
1

detected by
an unknotting move
1-8t+22t^2-29t^3+22t^4-8t^5+t^6
Seifert matrix of 12n_0584
-1 -1 0 0 -1 0
0 -1 0 1 -1 1
0 0 1 0 0 0
0 0 0 1 0 1
0 0 -1 1 -1 0
0 0 1 0 0 -1
1
Generator of the Alexander module
(2-t-t^2,0,0,-t,1,1)
the Blanchfield form on it
t^-2-7t^-1+13-7t+t^2
91
First homology
of the double branched cover of 12n_0584
Z/91
-2 2
12n_0585
3

detected by
the signature
4-9t+10t^2-9t^3+10t^4-9t^5+4t^6
Seifert matrix of 12n_0585
-1 0 0 0 0 0
1 -2 1 1 -1 0
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
1 0 1 0 -2 0
0 -1 0 0 -1 -1
1 or 2
55
First homology
of the double branched cover of 12n_0585
Z/55
-6 6
12n_0586
1

detected by
an unknotting move
-1+8t-24t^2+35t^3-24t^4+8t^5-t^6
Seifert matrix of 12n_0586
-1 0 0 0 0 0
1 1 1 0 -1 0
-1 0 -1 0 0 0
-1 -1 -1 1 0 0
1 0 1 0 1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,-t,0,1,0,0)
the Blanchfield form on it
2t^-2-9t^-1+15-9t+2t^2
101
First homology
of the double branched cover of 12n_0586
Z/101
0 0
12n_0587
1

detected by
an unknotting move
-1+10t-28t^2+39t^3-28t^4+10t^5-t^6
Seifert matrix of 12n_0587
-1 0 0 0 0 0
1 1 1 1 1 1
0 1 2 0 0 1
-1 0 0 -1 0 0
1 1 1 1 2 1
1 2 1 1 1 1
1
Generator of the Alexander module
(0,0,0,-2t+t^2,0,1+5t-5t^2+t^3)
the Blanchfield form on it
-1
117
First homology
of the double branched cover of 12n_0587
Z/117
0 0
12n_0588
1

detected by
an unknotting move
-2+9t-19t^2+25t^3-19t^4+9t^5-2t^6
Seifert matrix of 12n_0588
0 0 -1 1 -1 1
1 -2 1 -2 1 -1
0 0 0 0 -1 1
1 -1 1 -2 1 -1
0 0 0 0 0 1
1 0 1 0 1 0
1
Generator of the Alexander module
(0,1-t,1,0,0,0)
the Blanchfield form on it
-t^-4+7t^-3-22t^-2+42t^-1-52+42t-22t^2+7t^3-t^4
85
First homology
of the double branched cover of 12n_0588
Z/85
0 0
12n_0589
2

detected by
the signature
-2+12t-26t^2+33t^3-26t^4+12t^5-2t^6
Seifert matrix of 12n_0589
-1 0 -1 -1 0 -1
0 -1 -1 0 -1 -1
0 0 -2 -1 0 -2
0 0 -2 -1 -1 -2
0 0 0 -1 0 0
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(-2t^2+2t^3,1+4t^2-t^3,0,0,0,-t)
the Blanchfield form on it
-2t^-2+6t^-1-8+6t-2t^2
113
First homology
of the double branched cover of 12n_0589
Z/113
-4 4
12n_0590
3

detected by
the signature
-1+4t-4t^2+2t^3-t^4+2t^5-4t^6+4t^7-t^8
Seifert matrix of 12n_0590
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 1 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
-1 1 0 -1 -1 -1 -1 -1
-1 0 0 -1 0 -1 0 -1
1 or 2
23
First homology
of the double branched cover of 12n_0590
Z/23
-6 6
12n_0591
3

detected by
the signature
1-2t^2+2t^3-t^4+2t^5-2t^6+t^8
Seifert matrix of 12n_0591
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
-1 1 0 -1 -1 -1 -1 -1
-1 0 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-2t^-1+3-2t+t^3
7
First homology
of the double branched cover of 12n_0591
Z/7
-6 6
12n_0592
2

detected by
the Nakanishi index
1-4t+8t^2-8t^3+7t^4-8t^5+8t^6-4t^7+t^8
Seifert matrix of 12n_0592
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 1 1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 1 0
-1 0 0 -1 1 1 1 1
-1 1 0 -1 0 0 1 0
-1 0 0 -1 1 0 1 1
2
49
First homology
of the double branched cover of 12n_0592
Z/7+Z/7
4 4
12n_0593
2

detected by
the signature
-2+9t-13t^2+13t^3-13t^4+9t^5-2t^6
Seifert matrix of 12n_0593
-1 0 0 0 0 0
0 1 0 0 0 0
-1 1 -1 -1 0 0
-1 0 0 -1 0 0
-1 1 0 -1 -1 1
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-1-3+2t
61
First homology
of the double branched cover of 12n_0593
Z/61
-4 4
12n_0594
2

detected by
the signature
2-t-5t^2+9t^3-5t^4-t^5+2t^6
Seifert matrix of 12n_0594
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 1 -1 -1 0 0
-1 0 0 -1 0 0
-1 1 0 -1 -1 1
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,0,1,0,-1,0)
the Blanchfield form on it
t^-2+t^-1-2+t+t^2
13
First homology
of the double branched cover of 12n_0594
Z/13
-4 4
12n_0595
1

detected by
an unknotting move
2-9t+21t^2-27t^3+21t^4-9t^5+2t^6
Seifert matrix of 12n_0595
-1 0 0 0 0 0
0 1 0 0 0 0
-1 1 1 -1 0 0
-1 0 0 -1 0 0
-1 1 0 -1 1 0
1 0 0 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,1,-1)
the Blanchfield form on it
-t^-1+1-t
91
First homology
of the double branched cover of 12n_0595
Z/91
2 2
12n_0596
2

detected by
the Lickorish test
3-11t+21t^2-25t^3+21t^4-11t^5+3t^6
Seifert matrix of 12n_0596
-1 0 0 0 0 0
1 2 1 1 0 1
0 1 2 0 -1 1
-1 0 0 -1 0 0
0 0 0 0 1 0
1 2 1 1 -1 2
1
Generator of the Alexander module
(0,1,0,0,4,-2)
the Blanchfield form on it
-42t^-2+143t^-1-215+143t-42t^2
95
First homology
of the double branched cover of 12n_0596
Z/95
2 2
12n_0597
1

detected by
an unknotting move
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 12n_0597
0 0 1 0 -1 1
1 -2 -2 -2 1 -1
1 -1 -2 -1 1 -1
1 -1 -2 -2 1 -1
0 0 0 0 0 1
1 0 0 0 1 0
1
Generator of the Alexander module
(0,0,1-t^2,-t+t^3,-t,-t^2)
the Blanchfield form on it
1
75
First homology
of the double branched cover of 12n_0597
Z/75
-2 2
12n_0598
2

detected by
the Nakanishi index
1-8t+24t^2-33t^3+24t^4-8t^5+t^6
Seifert matrix of 12n_0598
-1 0 1 0 0 0
0 -1 0 -1 0 0
0 1 -1 1 -1 1
0 0 0 -1 0 0
0 -1 0 -1 1 0
0 1 0 0 0 1
2
99
First homology
of the double branched cover of 12n_0598
Z/33+Z/3
-2 2
12n_0599
1

detected by
an unknotting move
-1+4t-7t^2+10t^3-11t^4+10t^5-7t^6+4t^7-t^8
Seifert matrix of 12n_0599
-1 0 0 0 0 0 0 0
0 1 0 0 1 0 1 0
-1 1 -1 -1 1 0 1 0
-1 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
-1 1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,1+t+t^2,t+2t^2-2t^3,-2t+t^2-t^3,1+t,-t-t^2-t^3,0,-t-t^2)
the Blanchfield form on it
t^-2-2t^-1+3-2t+t^2
55
First homology
of the double branched cover of 12n_0599
Z/55
-2 2
12n_0600
3

detected by
the signature
4-9t+12t^2-13t^3+12t^4-9t^5+4t^6
Seifert matrix of 12n_0600
-1 0 0 0 0 0
1 -2 1 0 -1 0
-1 0 -1 0 0 0
0 -1 0 -1 -1 0
1 0 1 0 -2 0
0 -1 0 -1 -1 -1
2
63
First homology
of the double branched cover of 12n_0600
Z/21+Z/3
-6 6
12n_0601
2

detected by
the Nakanishi index
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 12n_0601
-1 0 0 0 0 0
1 -1 1 1 0 1
-1 0 -1 0 0 0
0 0 0 1 0 1
1 1 1 1 -1 1
0 0 0 0 0 1
2
27
First homology
of the double branched cover of 12n_0601
Z/9+Z/3
-2 2
12n_0602
2

detected by
the Nakanishi index
1-9t+24t^2-31t^3+24t^4-9t^5+t^6
Seifert matrix of 12n_0602
-1 0 0 0 0 0
1 1 1 0 -1 0
-1 0 -1 0 0 0
0 -1 0 -1 -1 0
1 0 1 0 1 0
0 -1 0 -1 -1 -1
2
99
First homology
of the double branched cover of 12n_0602
Z/33+Z/3
-2 2
12n_0603
3

detected by
the signature
-1+4t-4t^2+3t^4-4t^6+4t^7-t^8
Seifert matrix of 12n_0603
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 1 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 0 -1 0
-1 0 0 -1 0 -1 0 0
-1 0 -1 -1 0 0 -1 0
-1 1 0 -1 0 -1 0 -1
1 or 2
15
First homology
of the double branched cover of 12n_0603
Z/15
-6 6
12n_0604
2

detected by
the Nakanishi index
1-4t+10t^2-16t^3+19t^4-16t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0604
-1 0 -1 -1 -1 -1 0 -1
0 1 0 0 0 0 1 0
0 1 0 -1 0 -1 1 -1
0 0 -1 0 -1 -1 0 -1
0 1 -1 -1 0 -1 1 -1
0 1 0 -1 0 0 1 -1
0 0 0 0 0 0 1 0
0 0 -1 0 -1 -1 0 0
2
81
First homology
of the double branched cover of 12n_0604
Z/27+Z/3
4 4
12n_0605
2

detected by
the Nakanishi index
-1+2t-4t^3+7t^4-4t^5+2t^7-t^8
Seifert matrix of 12n_0605
-1 0 -1 -1 -1 -1 0 -1
0 1 0 0 0 0 1 0
0 1 0 -1 0 -1 1 -1
0 0 -1 -2 -1 -1 0 -2
0 1 -1 -1 0 -1 1 -1
0 1 0 -1 0 0 1 -1
0 0 0 0 0 0 1 0
0 0 -1 -1 -1 -1 0 -2
2
9
First homology
of the double branched cover of 12n_0605
Z/3+Z/3
0 0
12n_0606
1

detected by
an unknotting move
2-8t+18t^2-23t^3+18t^4-8t^5+2t^6
Seifert matrix of 12n_0606
-1 1 -1 -1 -1 0
0 1 1 1 1 1
0 0 0 -1 -1 -1
0 1 -1 0 -1 0
0 0 0 -1 0 -1
0 1 0 1 0 2
1
Generator of the Alexander module
(1-t,0,0,0,1,0)
the Blanchfield form on it
2t^-2-6t^-1+8-6t+2t^2
79
First homology
of the double branched cover of 12n_0606
Z/79
2 2
12n_0607
1

detected by
an unknotting move
2-7t+13t^2-15t^3+13t^4-7t^5+2t^6
Seifert matrix of 12n_0607
0 1 -1 -1 -1 1
1 -2 1 1 1 -1
0 0 0 0 -1 1
0 0 -1 0 -1 1
0 0 0 0 0 1
1 0 1 1 1 0
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+6t^-1-9+6t-2t^2
59
First homology
of the double branched cover of 12n_0607
Z/59
2 2
12n_0608
1

detected by
an unknotting move
3-10t+15t^2-10t^3+3t^4
Seifert matrix of 12n_0608
0 1 1 1
1 -2 -1 -1
0 0 1 -1
1 0 -1 0
1
Generator of the Alexander module
(0,1,0,1)
the Blanchfield form on it
-t^-1+2-t
41
First homology
of the double branched cover of 12n_0608
Z/41
0 0
12n_0609
2

detected by
the signature
1-4t+7t^2-6t^3+5t^4-6t^5+7t^6-4t^7+t^8
Seifert matrix of 12n_0609
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 1 -1 -1 0 0 1 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
-1 0 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,t-t^2+2t^3-t^4-3t^5+3t^6-t^7,2+3t-2t^2-t^3-t^4-t^5+2t^6-t^7,0,1+t^2+t^3-4t^4+2t^6-t^7,0,-1+t-2t^2+t^3+3t^4-3t^5+t^6,-t^2+t^3-2t^4+t^5+3t^6-3t^7+t^8)
the Blanchfield form on it
x
41
First homology
of the double branched cover of 12n_0609
Z/41
-4 4
12n_0610
1

detected by
an unknotting move
1-4t+8t^2-12t^3+15t^4-12t^5+8t^6-4t^7+t^8
Seifert matrix of 12n_0610
-1 0 0 0 0 0 0 0
0 1 0 0 1 0 1 1
-1 1 -1 -1 1 0 1 1
-1 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 1 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 1 0 1 1
1
Generator of the Alexander module
(0,-1,-1,1,0,0,0,0)
the Blanchfield form on it
1
65
First homology
of the double branched cover of 12n_0610
Z/65
0 0
12n_0611
2

detected by
the Nakanishi index
2-9t+17t^2-19t^3+17t^4-9t^5+2t^6
Seifert matrix of 12n_0611
-1 0 0 0 0 0
0 1 0 0 -1 0
-1 1 -1 -1 -1 0
-1 0 0 -1 0 0
0 0 0 0 2 0
-1 1 0 -1 0 -1
2
75
First homology
of the double branched cover of 12n_0611
Z/15+Z/5
-2 2
12n_0612
2

detected by
the Lickorish test
1-9t+23t^2-29t^3+23t^4-9t^5+t^6
Seifert matrix of 12n_0612
-1 1 0 1 -1 0
0 -2 -1 -1 0 0
0 0 1 0 0 0
0 -1 0 -2 1 0
0 1 0 1 0 0
0 -1 0 -1 0 -1
1 or 2
95
First homology
of the double branched cover of 12n_0612
Z/95
-2 2
12n_0613
1

detected by
an unknotting move
1-6t+15t^2-23t^3+27t^4-23t^5+15t^6-6t^7+t^8
Seifert matrix of 12n_0613
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
0 -1 -1 0 -1 0 0 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 0 1 0
0 0 0 0 0 1 0 0
0 0 0 0 0 1 1 0
0 -1 -1 0 0 0 0 -1
1
Generator of the Alexander module
(18-58t-129t^2+269t^3-48t^4-131t^5+9t^6,-19-28t+12t^2-68t^3+16t^4+90t^5-6t^6,-3-5t+5t^2-t^3,-2t-3t^2-3t^3+t^4-t^5,4-11t-26t^2+63t^3-12t^4-28t^5+2t^6,0,7+10t-t^2+33t^3-8t^4-45t^5+3t^6,2t+4t^2)
the Blanchfield form on it
x
117
First homology
of the double branched cover of 12n_0613
Z/117
0 2
12n_0614
1

detected by
an unknotting move
-1+6t-17t^2+25t^3-17t^4+6t^5-t^6
Seifert matrix of 12n_0614
0 -1 -1 0 0 0
-1 -2 -2 -1 0 -1
-1 -1 0 -1 0 -1
0 0 0 -1 0 0
1 0 0 0 -1 1
-1 -1 -1 -1 0 0
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-1
73
First homology
of the double branched cover of 12n_0614
Z/73
0 0
12n_0615
2

detected by
the Lickorish test
-1+6t-15t^2+19t^3-17t^4+19t^5-15t^6+6t^7-t^8
Seifert matrix of 12n_0615
-1 -1 -1 -1 1 0 -1 1
0 -1 -1 -1 0 0 0 1
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 -1 0 0 0 -1 -1 0
0 -1 -1 -1 1 0 -1 1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(2t^2+2t^3-t^4+2t^6+2t^7-6t^8+12t^9-11t^10+5t^11-2t^12,0,-1-3t-t^2+2t^3-t^4+2t^5-t^6+t^8+5t^9-4t^11+3t^12-2t^13,-1-3t-2t^2-t^3-3t^4+t^5-4t^6+t^7-3t^8+6t^9-3t^10+2t^11,2t+4t^2+2t^3+5t^4+3t^6+t^7+6t^8-6t^9-t^10+t^11-2t^12,t+t^3+3t^4-t^5-2t^6+4t^7-t^8-5t^9+5t^10-2t^11,1+t+t^2+t^3-t^4+4t^5-6t^6+9t^7-9t^
the Blanchfield form on it
x
99
First homology
of the double branched cover of 12n_0615
Z/99
-2 2
12n_0616
1

detected by
an unknotting move
-1+6t-15t^2+21t^3-15t^4+6t^5-t^6
Seifert matrix of 12n_0616
0 -1 -1 0 0 -1
0 1 0 0 0 0
-2 -1 -1 -1 -1 -1
-1 -1 -1 -1 0 0
-1 -1 -1 -1 -1 0
0 1 0 0 0 1
1
Generator of the Alexander module
(0,1,6-4t+t^2,-t+t^2,0,0)
the Blanchfield form on it
-1
65
First homology
of the double branched cover of 12n_0616
Z/65
0 0
12n_0617
2

detected by
the signature
-1+3t-3t^3+3t^5-t^6
Seifert matrix of 12n_0617
0 -1 -1 0 0 -1
0 1 0 0 0 0
-2 -1 -1 -1 -1 -1
-1 -1 -1 0 0 0
-1 -1 -1 -1 0 0
0 1 0 0 0 1
2
5
First homology
of the double branched cover of 12n_0617
Z/5
4 4
12n_0618
1

detected by
an unknotting move
1-6t+15t^2-21t^3+21t^4-21t^5+15t^6-6t^7+t^8
Seifert matrix of 12n_0618
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
0 0 1 0 0 0 0 0
-1 0 0 -1 -1 -1 0 0
0 0 0 0 -1 0 -1 0
0 0 0 0 -1 -1 -1 0
0 0 1 0 0 0 1 0
0 0 -1 0 -1 -1 -1 -1
1
Generator of the Alexander module
(0,-4t+3t^2+2t^3-t^4,t-t^2,-1-3t+2t^2+2t^3-t^4,1-2t-t^2+3t^3-t^4,-t+2t^3-t^4,1+t-3t^2+t^3,1-2t-t^2+3t^3-t^4)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-9+8t-4t^2+t^3
107
First homology
of the double branched cover of 12n_0618
Z/107
-2 2
12n_0619
2

detected by
the signature
-1+6t-14t^2+15t^3-13t^4+15t^5-14t^6+6t^7-t^8
Seifert matrix of 12n_0619
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
0 0 1 0 0 0 0 0
-1 0 0 -1 -1 -1 0 0
0 0 0 0 1 1 -1 1
0 0 0 0 0 1 -1 1
0 0 1 0 0 0 1 0
0 0 -1 0 0 0 -1 1
1 or 2
85
First homology
of the double branched cover of 12n_0619
Z/85
4 4
12n_0620
1

detected by
an unknotting move
2-13t+34t^2-45t^3+34t^4-13t^5+2t^6
Seifert matrix of 12n_0620
2 0 1 1 2 0
0 -1 0 0 1 1
0 0 -1 0 0 1
0 0 1 0 1 0
1 0 2 1 2 0
1 0 1 1 2 -1
1
Generator of the Alexander module
(0,3-3t+t^2,0,0,1,0)
the Blanchfield form on it
1
143
First homology
of the double branched cover of 12n_0620
Z/143
-2 2
12n_0621
2

detected by
the Lickorish test
1-7t+23t^2-33t^3+23t^4-7t^5+t^6
Seifert matrix of 12n_0621
0 1 0 1 -1 1
1 0 1 -1 1 -2
-1 1 -1 0 -1 2
0 0 0 1 0 0
0 0 0 0 1 0
1 -1 0 -2 2 -2
1 or 2
95
First homology
of the double branched cover of 12n_0621
Z/95
2 2
12n_0622
2

detected by
the Nakanishi index
-1+6t-14t^2+19t^3-19t^4+19t^5-14t^6+6t^7-t^8
Seifert matrix of 12n_0622
-1 0 0 1 -1 0 -1 0
-1 1 -1 0 0 -1 -1 1
-1 0 -1 0 -1 -1 -1 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
-1 0 0 1 -1 -1 -1 0
0 0 0 1 -1 0 -1 0
0 0 -1 0 0 -1 0 1
2
99
First homology
of the double branched cover of 12n_0622
Z/33+Z/3
-2 2
12n_0623
2

detected by
the signature
1-5t+10t^2-8t^3+5t^4-8t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0623
-1 0 0 0 0 0 0 0
0 -1 -1 0 -1 1 0 0
-1 0 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 0 1 0 0
0 -1 -1 0 -1 1 -1 0
0 -1 0 0 -1 0 0 1
1 or 2
53
First homology
of the double branched cover of 12n_0623
Z/53
-4 4
12n_0624
2

detected by
the signature
-1+3t-6t^3+9t^4-6t^5+3t^7-t^8
Seifert matrix of 12n_0624
-1 0 0 0 0 0 0 0
0 -1 -1 0 -1 1 0 0
-1 0 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 0 -1 0 0
0 -1 -1 0 -1 1 -1 0
0 -1 0 0 -1 0 0 1
1
Generator of the Alexander module
(0,1,0,0,1,0,0,t)
the Blanchfield form on it
-t^-3+2t^-1-3+2t-t^3
13
First homology
of the double branched cover of 12n_0624
Z/13
-4 4
12n_0625
1

detected by
an unknotting move
-1+5t-12t^2+18t^3-19t^4+18t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0625
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
-1 1 1 -1 1 0 1 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 0 1 0
0 0 0 0 0 1 0 0
0 0 0 0 0 1 1 0
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1+2t-t^2,0,0,-1-2t-t^2+t^3)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-5+5t-3t^2+t^3
91
First homology
of the double branched cover of 12n_0625
Z/91
2 2
12n_0626
3

detected by
the new u==2 criterion
-2+15t-36t^2+47t^3-36t^4+15t^5-2t^6
Seifert matrix of 12n_0626
0 1 1 1 -1 1
1 0 -2 -1 1 -1
1 -1 -2 -2 2 -2
0 0 0 1 0 1
0 0 0 0 1 0
0 0 0 -1 1 1
2
153
First homology
of the double branched cover of 12n_0626
Z/51+Z/3
4 4
12n_0627
1

detected by
an unknotting move
1-4t+12t^2-25t^3+33t^4-25t^5+12t^6-4t^7+t^8
Seifert matrix of 12n_0627
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
-1 1 1 -1 0 0 1 1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 -1 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 1 1 0
-1 1 0 -1 0 0 1 1
1
Generator of the Alexander module
(0,2-t-t^2+t^3,-2t-t^2+4t^3-t^4-2t^5+t^6,-2t+t^2+t^3-t^4,1-2t-t^2+3t^3+t^4-3t^5+t^6,-t-t^2+t^3+t^4-t^5,1-3t^2+2t^3+t^4-t^5,2-t-t^2+t^3)
the Blanchfield form on it
x
117
First homology
of the double branched cover of 12n_0627
Z/117
0 0
12n_0628
1

detected by
an unknotting move
-1+8t-25t^2+37t^3-25t^4+8t^5-t^6
Seifert matrix of 12n_0628
0 -1 0 -1 -1 -1
-1 0 0 0 -1 -1
-1 -1 -1 -1 -1 0
0 0 0 -1 0 -1
-2 -1 -1 -1 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,1,0)
the Blanchfield form on it
1
105
First homology
of the double branched cover of 12n_0628
Z/105
0 0
12n_0629
1

detected by
an unknotting move
1-4t+6t^2-5t^3+6t^4-4t^5+t^6
Seifert matrix of 12n_0629
1 0 1 0 0 -1
0 1 1 1 0 -1
0 0 1 0 0 0
1 1 1 0 1 -1
-1 0 0 0 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
27
First homology
of the double branched cover of 12n_0629
Z/27
2 2
12n_0630
2

detected by
the Lickorish test
1-4t+3t^2+t^3+3t^4-4t^5+t^6
Seifert matrix of 12n_0630
0 -1 0 -1 -1 -1
-1 0 0 0 -1 -1
-1 -1 -1 -1 -1 0
0 0 0 -1 0 -1
-2 -1 -1 -1 -1 -1
0 0 0 0 0 -1
2
15
First homology
of the double branched cover of 12n_0630
Z/15
-2 2
12n_0631
1

detected by
an unknotting move
-1+6t-19t^2+29t^3-19t^4+6t^5-t^6
Seifert matrix of 12n_0631
1 0 1 0 0 -1
0 0 1 1 0 -1
0 0 1 0 0 0
1 1 1 0 1 -1
-1 0 0 0 -1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,1+t-t^2,0,-3-4t+3t^2,0,0)
the Blanchfield form on it
t^-2-4t^-1+10-4t+t^2
81
First homology
of the double branched cover of 12n_0631
Z/81
0 0
12n_0632
1

detected by
an unknotting move
1-7t+19t^2-30t^3+33t^4-30t^5+19t^6-7t^7+t^8
Seifert matrix of 12n_0632
1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 -1
-1 0 -1 -1 0 -1 0 -1
0 0 0 1 1 0 -1 1
0 0 0 0 1 0 0 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 1 0 -1 1
1
Generator of the Alexander module
(12t^2-9t^3+79t^4-113t^5+21t^6+35t^7-29t^8+6t^9,-54t+6t^2+136t^3-146t^4+70t^5-12t^6,7-118t-108t^2+539t^3-157t^4-512t^5+559t^6-247t^7+39t^8,27t-57t^2+46t^3-19t^4+3t^5,-6+9t-34t^2+33t^3+11t^4-27t^5+16t^6-3t^7,-54t^2+33t^3+187t^4-328t^5+235t^6-85t^7+12t^8,9+11t-47t^2+43t^3-19t^4+3t^5,0)
the Blanchfield form on it
x
147
First homology
of the double branched cover of 12n_0632
Z/147
2 2
12n_0633
1

detected by
an unknotting move
-2+10t-22t^2+29t^3-22t^4+10t^5-2t^6
Seifert matrix of 12n_0633
-1 -1 -1 -1 -1 0
0 1 0 1 0 0
0 1 2 1 0 0
0 1 1 0 0 0
0 0 -1 -1 -1 0
0 1 1 1 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
1
97
First homology
of the double branched cover of 12n_0633
Z/97
0 0
12n_0634
1

detected by
an unknotting move
1-5t+11t^2-13t^3+11t^4-5t^5+t^6
Seifert matrix of 12n_0634
0 -1 0 -1 0 -1
-2 -1 -1 -1 -1 -1
-1 -1 -1 -1 0 0
0 0 0 -1 0 -1
-1 -1 -1 -1 -1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-9t^-1+15-9t+2t^2
47
First homology
of the double branched cover of 12n_0634
Z/47
-2 2
12n_0635
1

detected by
an unknotting move
1-7t+19t^2-32t^3+39t^4-32t^5+19t^6-7t^7+t^8
Seifert matrix of 12n_0635
-1 0 0 1 -1 0 -1 0
-1 1 -1 0 0 1 -1 1
-1 0 -1 0 -1 0 -1 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 -1 0 0 1 0 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 1 0 1
1
Generator of the Alexander module
(0,0,-1,0,0,1,0,-2t+t^2)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
157
First homology
of the double branched cover of 12n_0635
Z/157
0 0
12n_0636
2

detected by
the Nakanishi index
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 12n_0636
-1 0 0 0 0 -1
0 1 1 -1 0 -1
-1 0 0 -1 0 -2
-1 0 0 -2 -1 -2
0 0 0 0 1 0
-1 0 -1 0 0 -1
2
81
First homology
of the double branched cover of 12n_0636
Z/9+Z/9
0 0
12n_0637
2

detected by
the Nakanishi index
2-13t+32t^2-41t^3+32t^4-13t^5+2t^6
Seifert matrix of 12n_0637
-1 0 -1 0 0 0
0 -2 -1 -2 1 0
0 -1 -2 -1 1 -1
0 -1 -1 -2 1 0
0 0 0 0 1 0
0 -1 -1 0 0 0
2
135
First homology
of the double branched cover of 12n_0637
Z/45+Z/3
-2 2
12n_0638
3

detected by
the signature
2-3t+2t^2-t^3+2t^4-3t^5+2t^6
Seifert matrix of 12n_0638
-1 0 0 0 1 0
0 -2 0 -1 0 -1
0 -1 -1 -1 -1 -1
0 -1 0 -1 0 0
0 -1 0 0 -2 0
0 -1 0 -1 0 -1
1 or 2
15
First homology
of the double branched cover of 12n_0638
Z/15
-6 6
12n_0639
3

detected by
the signature
-1+4t-5t^2+5t^3-5t^4+5t^5-5t^6+4t^7-t^8
Seifert matrix of 12n_0639
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 1 -1 -1 -1 0 -1 0
-1 1 0 -1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 0 0
-1 1 0 -1 -1 0 -1 0
-1 1 0 0 -1 -1 0 -1
1 or 2
35
First homology
of the double branched cover of 12n_0639
Z/35
-6 6
12n_0640
3

detected by
the signature
1-3t^2+7t^3-9t^4+7t^5-3t^6+t^8
Seifert matrix of 12n_0640
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 -1 -1 -1 0 -1 0
-1 1 0 -1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 0 0
-1 1 0 -1 -1 0 -1 0
-1 1 0 0 -1 -1 0 -1
1 or 2
27
First homology
of the double branched cover of 12n_0640
Z/27
-6 6
12n_0641
2

detected by
the signature
1-4t+9t^2-13t^3+15t^4-13t^5+9t^6-4t^7+t^8
Seifert matrix of 12n_0641
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 1 1 0 -1 0 0 0
-1 1 1 1 -1 0 1 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 1 0 1
-1 1 1 0 -1 0 1 0
-1 1 0 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+9-8t+4t^2-t^3
69
First homology
of the double branched cover of 12n_0641
Z/69
4 4
12n_0642
3

detected by
the Nakanishi index
1+7t-15t^2+7t^3+t^4
Seifert matrix of 12n_0642
1 0 0 0
1 1 0 -1
1 -1 1 -1
1 0 0 1
3
27
First homology
of the double branched cover of 12n_0642
Z/3+Z/3+Z/3
2 2
12n_0643
2

detected by
the Nakanishi index
-2+8t-10t^2+9t^3-10t^4+8t^5-2t^6
Seifert matrix of 12n_0643
-1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
1 -1 1 0 -2 0
-1 1 -1 -1 0 -1
2
49
First homology
of the double branched cover of 12n_0643
Z/7+Z/7
-4 4
12n_0644
3

detected by
the signature
2-2t+t^3-2t^5+2t^6
Seifert matrix of 12n_0644
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
1 -1 1 0 -2 0
-1 1 -1 -1 0 -1
1 or 2
7
First homology
of the double branched cover of 12n_0644
Z/7
-6 6
12n_0645
1

detected by
an unknotting move
2-8t+16t^2-19t^3+16t^4-8t^5+2t^6
Seifert matrix of 12n_0645
-1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 1 0 1
1 -1 1 0 2 0
-1 1 -1 0 0 1
1
Generator of the Alexander module
(0,0,1,2,-1,1)
the Blanchfield form on it
-1
71
First homology
of the double branched cover of 12n_0645
Z/71
2 2
12n_0646
1

detected by
an unknotting move
-1+5t-12t^2+21t^3-25t^4+21t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0646
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1
-1 1 1 -1 -1 0 0 1
-1 0 0 0 -1 0 0 0
-1 0 1 0 -1 -1 0 1
-1 1 1 0 -1 -1 -1 1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(0,1+3t,0,-1+t+3t^2,t^2,2+t-2t^2,-1-t-2t^2,0)
the Blanchfield form on it
-t^-3+3t^-2-5t^-1+8-5t+3t^2-t^3
103
First homology
of the double branched cover of 12n_0646
Z/103
-2 2
12n_0647
3

detected by
the signature
1-3t^2+6t^3-7t^4+6t^5-3t^6+t^8
Seifert matrix of 12n_0647
-1 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 -1
0 0 -1 0 0 0 0 0
-1 1 1 -1 -1 0 0 1
-1 0 0 0 -1 0 0 0
-1 0 1 0 -1 -1 0 1
-1 1 1 0 -1 -1 -1 1
0 0 -1 0 0 0 0 -1
1 or 2
23
First homology
of the double branched cover of 12n_0647
Z/23
-6 6
12n_0648
3

detected by
the signature
-1+4t-3t^2-t^3+3t^4-t^5-3t^6+4t^7-t^8
Seifert matrix of 12n_0648
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 -1
0 0 1 0 0 0 0 0
-1 0 1 -1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 0 0
0 -1 0 0 0 -1 -1 -1
-1 0 1 0 -1 -1 0 -1
1 or 2
11
First homology
of the double branched cover of 12n_0648
Z/11
-6 6
12n_0649
2

detected by
the signature
1-5t+11t^2-14t^3+15t^4-14t^5+11t^6-5t^7+t^8
Seifert matrix of 12n_0649
-1 0 0 0 0 0 0 0
0 -1 -1 -1 0 0 0 -1
-1 0 -1 -1 -1 0 -1 0
0 0 0 1 0 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 -1 0
0 0 0 1 0 0 1 0
-1 0 -1 -1 -1 0 -1 -1
1
Generator of the Alexander module
(0,-2+2t^2,-t,0,1-t^2,t-t^2,0,-2t)
the Blanchfield form on it
11t^-3-59t^-2+109t^-1-135+109t-59t^2+11t^3
77
First homology
of the double branched cover of 12n_0649
Z/77
-4 4
12n_0650
1

detected by
an unknotting move
1-4t+7t^2-4t^3+t^4
Seifert matrix of 12n_0650
0 1 1 0
1 0 0 0
0 0 1 0
0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
1
17
First homology
of the double branched cover of 12n_0650
Z/17
0 0
12n_0651
2

detected by
the Lickorish test
2-11t+28t^2-37t^3+28t^4-11t^5+2t^6
Seifert matrix of 12n_0651
-2 -1 -1 -1 0 -1
-1 0 0 -1 0 -1
-1 -1 -2 -1 0 -2
-2 -1 -1 -2 0 -1
1 0 0 1 1 1
-1 -1 -1 -1 0 -2
2
119
First homology
of the double branched cover of 12n_0651
Z/119
-2 2
12n_0652
2

detected by
A(F_3)
-1+5t-15t^2+30t^3-37t^4+30t^5-15t^6+5t^7-t^8
Seifert matrix of 12n_0652
-1 0 0 0 0 0 0 0
0 1 0 -1 0 0 0 0
-1 1 1 -1 -1 0 -1 1
0 0 0 -1 0 0 -1 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 -1 0
0 0 0 0 0 0 -1 0
-1 1 0 -1 -1 0 -1 1
2
139
First homology
of the double branched cover of 12n_0652
Z/139
-2 2
12n_0653
3

detected by
the signature
-1+4t-5t^2+6t^3-7t^4+6t^5-5t^6+4t^7-t^8
Seifert matrix of 12n_0653
-1 0 0 0 0 0 0 0
-1 -1 1 0 -1 -1 0 -1
0 0 1 0 0 0 0 0
-1 0 1 -1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 0 0
-1 -1 1 0 -1 -1 -1 -1
-1 0 1 0 -1 -1 0 -1
1 or 2
39
First homology
of the double branched cover of 12n_0653
Z/39
-6 6
12n_0654
3

detected by
the new u==2 criterion
-2+8t-9t^2+7t^3-9t^4+8t^5-2t^6
Seifert matrix of 12n_0654
-1 0 0 0 0 0
1 -2 -1 0 1 1
0 0 1 0 0 0
-1 0 1 -1 -1 0
-1 0 0 0 -1 0
-1 0 0 0 -1 -1
2
45
First homology
of the double branched cover of 12n_0654
Z/15+Z/3
-4 4
12n_0655
3

detected by
the signature
2-2t-t^2+3t^3-t^4-2t^5+2t^6
Seifert matrix of 12n_0655
-1 0 0 0 0 0
1 -2 -1 0 1 1
0 0 -1 0 0 0
-1 0 1 -1 -1 0
-1 0 0 0 -1 0
-1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,1-2t+2t^2,-t,-t,-1,-1)
the Blanchfield form on it
7t^-4-18t^-3+15t^-2+9t^-1-24+9t+15t^2-18t^3+7t^4
3
First homology
of the double branched cover of 12n_0655
Z/3
-6 6
12n_0656
1

detected by
an unknotting move
2-10t+23t^2-29t^3+23t^4-10t^5+2t^6
Seifert matrix of 12n_0656
-1 0 0 0 0 0
1 2 -1 0 1 0
0 0 1 0 0 0
-1 0 1 1 -1 0
-1 0 0 0 -1 0
-1 -1 0 0 -1 1
1
Generator of the Alexander module
(0,-2t,-1+t,t,0,1)
the Blanchfield form on it
-3t^-4+22t^-3-73t^-2+141t^-1-174+141t-73t^2+22t^3-3t^4
99
First homology
of the double branched cover of 12n_0656
Z/99
2 2
12n_0657 1 or 2
1-4t+9t^2-16t^3+21t^4-16t^5+9t^6-4t^7+t^8
Seifert matrix of 12n_0657
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
0 1 1 0 0 0 1 1
-1 1 1 -1 -1 0 1 1
-1 0 0 0 -1 0 0 0
-1 1 1 0 -1 -1 0 1
0 0 0 0 0 0 1 0
0 1 0 0 0 0 1 1
1 or 2
81
First homology
of the double branched cover of 12n_0657
Z/81
0 0
12n_0658
2

detected by
the signature
1-5t+12t^2-17t^3+19t^4-17t^5+12t^6-5t^7+t^8
Seifert matrix of 12n_0658
-1 0 0 0 0 0 0 0
-1 -1 1 0 -1 -1 0 1
0 0 1 0 0 0 0 1
-1 0 1 -1 -1 0 0 1
-1 0 0 0 -1 0 0 0
-1 0 1 0 -1 -1 0 0
-1 -1 1 0 -1 -1 -1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-9+8t-4t^2+t^3
89
First homology
of the double branched cover of 12n_0658
Z/89
-4 4
12n_0659
2

detected by
the signature
-2+10t-16t^2+17t^3-16t^4+10t^5-2t^6
Seifert matrix of 12n_0659
-1 0 0 0 0 0
0 1 0 0 0 0
0 1 -1 0 0 -1
-1 0 0 -1 0 0
-1 1 0 -1 -1 0
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,0,3-3t+t^2,-1+t,0,0)
the Blanchfield form on it
41t^-3-206t^-2+333t^-1-356+333t-206t^2+41t^3
73
First homology
of the double branched cover of 12n_0659
Z/73
-4 4
12n_0660
2

detected by
the signature
1+3t-12t^2+17t^3-12t^4+3t^5+t^6
Seifert matrix of 12n_0660
1 0 0 0 0 0
0 1 1 0 1 0
1 0 1 1 0 0
0 0 0 1 0 0
1 0 0 0 1 -1
1 0 0 1 0 1
2
45
First homology
of the double branched cover of 12n_0660
Z/45
4 4
12n_0661
2

detected by
the signature
-2+6t-5t^2+3t^3-5t^4+6t^5-2t^6
Seifert matrix of 12n_0661
-1 0 0 0 0 0
-1 -1 -1 0 0 -1
-1 0 -1 0 0 0
-1 -1 -1 -1 0 0
-1 0 -1 0 -1 -1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,0,0,t,1,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
29
First homology
of the double branched cover of 12n_0661
Z/29
-4 4
12n_0662
1

detected by
an unknotting move
2-8t+13t^2-13t^3+13t^4-8t^5+2t^6
Seifert matrix of 12n_0662
-1 0 0 0 0 0
-1 -1 -1 0 1 -1
-1 0 -1 0 0 0
-1 0 -1 -1 0 -1
0 0 0 0 1 0
0 0 0 0 -1 2
1
Generator of the Alexander module
(0,-6t^2+3t^3,0,2t^2-t^3,-2t+t^2,1-4t^2+2t^3)
the Blanchfield form on it
35t^-2-199t^-1+327-199t+35t^2
59
First homology
of the double branched cover of 12n_0662
Z/59
-2 2
12n_0663
1

detected by
an unknotting move
-1+6t-15t^2+23t^3-25t^4+23t^5-15t^6+6t^7-t^8
Seifert matrix of 12n_0663
-1 0 0 0 0 0 0 0
0 -1 -1 -1 0 -1 0 0
-1 0 -1 -1 -1 0 -1 0
0 0 0 1 0 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 -1 -1 -1 -1 -1 0
0 0 0 1 0 0 1 0
0 -1 0 0 0 -1 0 1
1
Generator of the Alexander module
(0,-4-t+9t^2-26t^3+31t^4-16t^5+3t^6,4-10t+16t^2-14t^3+6t^4-t^5,4-10t+16t^2-14t^3+6t^4-t^5,1-2t+t^2,-4+2t+4t^2-18t^3+22t^4-11t^5+2t^6,0,4-14t+18t^2-10t^3-12t^4+21t^5-11t^6+2t^7)
the Blanchfield form on it
x
115
First homology
of the double branched cover of 12n_0663
Z/115
-2 2
12n_0664
1

detected by
an unknotting move
1-7t+20t^2-34t^3+41t^4-34t^5+20t^6-7t^7+t^8
Seifert matrix of 12n_0664
1 0 0 0 0 0 -1 0
0 -1 -1 0 0 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 -1 0 -1 0 0 0
1 -1 0 0 -1 1 -1 1
0 -1 0 0 -1 0 -1 0
1 0 0 0 -1 0 -1 1
1
Generator of the Alexander module
(0,7-4t+15t^2-28t^3+27t^4-23t^5+6t^6,-10t+9t^2-10t^3+3t^4,0,7-4t+25t^2-37t^3+37t^4-26t^5+6t^6,7t-4t^2+15t^3-28t^4+27t^5-23t^6+6t^7,10+4t-t^2-10t^3+14t^4-20t^5+6t^6,-7-3t-8t^2+t^3-7t^4+3t^5)
the Blanchfield form on it
x
165
First homology
of the double branched cover of 12n_0664
Z/165
0 2
12n_0665
2

detected by
the Lickorish test
-2+10t-15t^2+10t^3-2t^4
Seifert matrix of 12n_0665
1 -1 -1 0
-2 4 3 0
-2 4 2 -1
0 0 0 1
1
Generator of the Alexander module
(1,-2,-2,0)
the Blanchfield form on it
t^-1-3+t
39
First homology
of the double branched cover of 12n_0665
Z/39
2 2
12n_0666
2

detected by
the Nakanishi index
1-4t+10t^2-16t^3+19t^4-16t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0666
0 -1 -1 -1 -1 0 -1 -1
-1 -2 -1 -1 -1 -1 -1 -1
-1 -2 -2 -1 -1 -1 -1 -1
0 0 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 0
-1 -2 -2 -1 -1 -2 -1 -1
0 -1 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 -1
2
81
First homology
of the double branched cover of 12n_0666
Z/27+Z/3
-4 4
12n_0667
1

detected by
an unknotting move
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 12n_0667
1 1 0 1 1 1
0 0 0 1 1 0
0 0 -1 1 1 0
0 1 0 0 0 0
0 1 0 1 -1 0
0 0 -1 1 1 -1
1
Generator of the Alexander module
(-t,0,-1,1,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
75
First homology
of the double branched cover of 12n_0667
Z/75
-2 2
12n_0668
2

detected by
the signature
1-5t+13t^2-21t^3+25t^4-21t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0668
1 0 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 0 -1 0 0 -1 0
0 -1 -1 0 -1 0 0 0
1 0 -1 0 -1 1 0 0
-1 1 1 0 1 -1 -1 0
0 0 0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,-1,0,1+t)
the Blanchfield form on it
3t^-3-14t^-2+31t^-1-38+31t-14t^2+3t^3
105
First homology
of the double branched cover of 12n_0668
Z/105
-4 4
12n_0669
2

detected by
the Nakanishi index
2-10t+23t^2-29t^3+23t^4-10t^5+2t^6
Seifert matrix of 12n_0669
1 0 0 0 -1 0
0 -1 0 0 0 0
0 -1 -1 0 0 0
1 -1 -1 -2 -1 1
0 -1 -1 0 -1 0
1 0 -1 0 -1 1
2
99
First homology
of the double branched cover of 12n_0669
Z/33+Z/3
-2 2
12n_0670
1

detected by
an unknotting move
1-2t+3t^2-4t^3+5t^4-4t^5+3t^6-2t^7+t^8
Seifert matrix of 12n_0670
-1 0 0 1 1 0 1 0
0 -1 0 -1 -1 0 -1 0
-1 0 -1 1 1 0 1 0
0 0 0 0 -1 1 -1 1
0 0 0 -1 0 0 -1 0
0 0 0 0 0 1 0 1
0 0 0 0 -1 1 0 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,1-t-t^2,1+t^3,3t^2-3t^3-2t^4,1+t,0,1+3t,-1)
the Blanchfield form on it
8t^-3-50t^-2+109t^-1-141+109t-50t^2+8t^3
25
First homology
of the double branched cover of 12n_0670
Z/25
0 0
12n_0671
3

detected by
the signature
-1+6t-13t^2+18t^3-19t^4+18t^5-13t^6+6t^7-t^8
Seifert matrix of 12n_0671
-1 0 0 1 1 0 1 0
0 -1 0 -1 -1 0 -1 0
-1 0 -1 1 1 0 1 0
0 0 0 -2 -1 0 -2 0
0 0 0 -1 0 0 -1 0
0 0 0 -1 0 -1 -1 0
0 0 0 -1 -1 0 -2 0
0 0 0 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,1,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-7t^-1+8-7t+5t^2-t^3
95
First homology
of the double branched cover of 12n_0671
Z/95
-6 6
12n_0672
2

detected by
the Lickorish test
1-4t+12t^2-17t^3+12t^4-4t^5+t^6
Seifert matrix of 12n_0672
-1 0 0 1 1 1
0 1 0 0 0 0
-1 0 -1 1 1 1
0 1 0 1 0 -1
0 1 0 0 1 0
0 1 0 0 0 1
1 or 2
51
First homology
of the double branched cover of 12n_0672
Z/51
2 2
12n_0673
1

detected by
an unknotting move
1-t+t^4-t^7+t^8
Seifert matrix of 12n_0673
-1 0 0 1 1 1 1 1
0 -1 0 -1 -1 -1 -1 -1
-1 0 -1 1 1 1 1 1
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,t,0,0,1,0,0)
the Blanchfield form on it
t^-1-2+t
5
First homology
of the double branched cover of 12n_0673
Z/5
0 2
12n_0674
3

detected by
the signature
-1+5t-10t^2+14t^3-15t^4+14t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0674
-1 0 0 1 1 1 1 1
0 -1 0 -1 -1 -1 -1 -1
-1 0 -1 1 1 1 1 1
0 0 0 -2 -2 -1 -2 -2
0 0 0 -1 -2 -1 -1 -2
0 0 0 -1 -1 0 -1 -1
0 0 0 -1 -2 -1 -2 -2
0 0 0 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-9t^-1+11-9t+5t^2-t^3
75
First homology
of the double branched cover of 12n_0674
Z/75
-6 6
12n_0675
1

detected by
an unknotting move
1-3t+6t^2-8t^3+9t^4-8t^5+6t^6-3t^7+t^8
Seifert matrix of 12n_0675
-1 0 0 1 1 1 1 1
0 -1 0 -1 -1 -1 -1 -1
-1 0 -1 1 1 1 1 1
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
0 0 0 -1 -1 -2 -1 -1
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
1
Generator of the Alexander module
(-2-2t+2t^2,1+t-t^2,t-t^2,0,0,0,0,0)
the Blanchfield form on it
27t^-3-54t^-2+55t^-1-34+55t-54t^2+27t^3
45
First homology
of the double branched cover of 12n_0675
Z/45
0 2
12n_0676
1

detected by
an unknotting move
2-2t-4t^2+9t^3-4t^4-2t^5+2t^6
Seifert matrix of 12n_0676
-1 0 0 1 -1 1
0 -1 0 -1 1 -1
-1 0 -1 1 -1 1
0 0 0 0 1 -1
0 0 0 0 1 1
0 0 0 -1 1 0
1
Generator of the Alexander module
(0,-t,-1,1,-1,1)
the Blanchfield form on it
2t^-2-2+2t^2
9
First homology
of the double branched cover of 12n_0676
Z/9
0 0
12n_0677
2

detected by
the signature
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 12n_0677
-1 0 0 1 -1 1
0 -1 0 -1 1 -1
-1 0 -1 1 -1 1
0 0 0 -2 2 -1
0 0 0 1 -3 1
0 0 0 -1 1 0
1
Generator of the Alexander module
(0,-1+t-2t^2,1-2t+2t^2-2t^3,0,1-t+2t^2,0)
the Blanchfield form on it
-35t^-4+223t^-3-625t^-2+1097t^-1-1304+1097t-625t^2+223t^3-35t^4
89
First homology
of the double branched cover of 12n_0677
Z/89
-4 4
12n_0678
1

detected by
an unknotting move
2-8t+18t^2-23t^3+18t^4-8t^5+2t^6
Seifert matrix of 12n_0678
-1 0 0 1 -1 1
0 -1 0 -1 1 -1
-1 0 -1 1 -1 1
0 0 0 0 1 -1
0 0 0 0 1 1
0 0 0 -1 1 -2
1
Generator of the Alexander module
(0,1,1,0,0,0)
the Blanchfield form on it
2t^-2-6t^-1+10-6t+2t^2
79
First homology
of the double branched cover of 12n_0678
Z/79
-2 2
12n_0679
4

detected by
the signature
1-t-t^2+4t^3-6t^4+7t^5-6t^6+4t^7-t^8-t^9+t^10
Seifert matrix of 12n_0679
-1 -1 0 -1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0 0 0
0 -1 0 -1 0 0 0 0 0 0
0 -1 0 -1 -1 -1 -1 0 -1 -1
0 -1 0 -1 0 -1 -1 0 0 -1
0 -1 0 -1 0 0 -1 0 0 0
0 0 0 0 -1 -1 -1 -1 -1 -1
0 -1 0 -1 0 -1 -1 0 -1 -1
0 -1 0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-4-t^-3-t^-2+4t^-1-5+4t-t^2-t^3+t^4
25
First homology
of the double branched cover of 12n_0679
Z/25
-8 8
12n_0680
3

detected by
the signature
2-3t-t^2+8t^3-11t^4+8t^5-t^6-3t^7+2t^8
Seifert matrix of 12n_0680
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 -1 0 -1 0 0 0 0
0 -1 0 -1 -1 1 -1 0
0 1 0 1 0 -2 1 0
0 -1 0 -1 0 0 -1 0
0 0 0 0 -1 1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,-2,0)
the Blanchfield form on it
-7t^-4+20t^-3-18t^-2-4t^-1+18-4t-18t^2+20t^3-7t^4
19
First homology
of the double branched cover of 12n_0680
Z/19
-6 6
12n_0681
1

detected by
an unknotting move
1-2t+3t^2-4t^3+5t^4-4t^5+3t^6-2t^7+t^8
Seifert matrix of 12n_0681
-1 0 0 1 1 0 1 1
0 -1 0 -1 -1 0 -1 -1
-1 0 -1 1 1 0 1 1
0 0 0 0 -1 1 -1 -1
0 0 0 0 0 1 0 -1
0 0 0 0 0 1 0 0
0 0 0 0 -1 1 0 -1
0 0 0 -1 -1 0 -1 0
1
Generator of the Alexander module
(0,-t+t^2-t^3-t^4+t^5,1+t-2t^2+5t^3-2t^5+t^6-t^7,2t^2-4t^3+4t^4-t^5-2t^6+2t^7-t^8,0,-2t+2t^2-t^4+t^5,0,0)
the Blanchfield form on it
x
25
First homology
of the double branched cover of 12n_0681
Z/25
0 0
12n_0682
3

detected by
the signature
-1+6t-13t^2+18t^3-19t^4+18t^5-13t^6+6t^7-t^8
Seifert matrix of 12n_0682
-1 0 0 1 1 0 1 1
0 -1 0 -1 -1 0 -1 -1
-1 0 -1 1 1 0 1 1
0 0 0 -2 -2 0 -2 -1
0 0 0 -1 -2 0 -1 -1
0 0 0 -1 -1 -1 -1 0
0 0 0 -1 -2 0 -2 -1
0 0 0 -1 -1 0 -1 0
1
Generator of the Alexander module
(0,1,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-7t^-1+8-7t+5t^2-t^3
95
First homology
of the double branched cover of 12n_0682
Z/95
-6 6
12n_0683
2

detected by
the signature
-1+4t-11t^2+18t^3-21t^4+18t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0683
1 0 0 0 0 0 -1 0
1 1 -1 -1 0 0 -1 -1
0 0 0 -1 1 0 0 -1
0 0 0 0 1 0 0 0
-1 0 1 1 0 0 1 1
1 1 -1 -1 0 1 -1 -1
0 0 -1 -1 1 0 -1 -1
0 0 0 -1 1 0 0 0
1
Generator of the Alexander module
(0,0,-1,0,0,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+6t^-1-7+6t-3t^2+t^3
89
First homology
of the double branched cover of 12n_0683
Z/89
4 4
12n_0684
2

detected by
the signature
1-4t+10t^2-15t^3+17t^4-15t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0684
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 0 0 0 0 -1 0
1 -1 -1 1 1 0 -2 0
1 -1 -1 0 1 0 -2 0
1 -1 -1 1 1 1 -2 0
0 -2 -1 0 0 0 -2 0
0 0 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-9t^-1+11-9t+4t^2-t^3
77
First homology
of the double branched cover of 12n_0684
Z/77
4 4
12n_0685
1

detected by
an unknotting move
2-8t+18t^2-23t^3+18t^4-8t^5+2t^6
Seifert matrix of 12n_0685
1 0 0 0 -1 0
0 -1 0 0 0 0
0 -1 0 0 -1 0
-1 1 1 2 2 0
0 -2 -1 0 -2 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+9t^-1-12+9t-4t^2+t^3
79
First homology
of the double branched cover of 12n_0685
Z/79
2 2
12n_0686
2

detected by
the signature
1-5t+13t^2-19t^3+21t^4-19t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0686
1 0 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
0 -1 -1 -1 0 -1 0 0
0 -1 0 -1 0 0 0 0
0 -1 -1 -1 -1 -1 0 0
0 -1 0 -1 0 -1 0 0
1 0 -1 -1 -1 -1 1 0
-1 1 1 1 1 1 -1 -1
1
Generator of the Alexander module
(0,2t+t^3,2t+2t^2-t^3+t^4-t^5,0,1+2t-2t^2-t^3-t^4-t^5,0,-2t^3-t^5,4t^2+2t^4)
the Blanchfield form on it
x
97
First homology
of the double branched cover of 12n_0686
Z/97
-4 4
12n_0687
1

detected by
an unknotting move
2-10t+25t^2-33t^3+25t^4-10t^5+2t^6
Seifert matrix of 12n_0687
1 0 -1 0 0 0
0 -1 0 0 0 0
0 -1 -1 1 0 0
0 1 0 1 0 0
1 0 -1 1 1 0
-1 1 1 -1 -1 2
1
Generator of the Alexander module
(0,1,1-t,-t,0,1)
the Blanchfield form on it
-2t^-2+7t^-1-12+7t-2t^2
107
First homology
of the double branched cover of 12n_0687
Z/107
2 2
12n_0688
4

detected by
the signature
-1+t+t^2-5t^3+9t^4-11t^5+9t^6-5t^7+t^8+t^9-t^10
Seifert matrix of 12n_0688
-1 -1 0 0 -1 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0 0 0
0 0 0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 0 0 0
0 -1 0 0 -1 -1 -1 0 0 -1
0 -1 0 0 -1 0 -1 0 0 0
0 0 0 -1 0 -1 -1 -1 -1 -1
0 0 0 0 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,-t,0,0)
the Blanchfield form on it
-t^-4-t^-3+8t^-2-16t^-1+19-16t+8t^2-t^3-t^4
37
First homology
of the double branched cover of 12n_0688
Z/37
-8 8
12n_0689
3

detected by
the signature
2-3t+5t^3-7t^4+5t^5-3t^7+2t^8
Seifert matrix of 12n_0689
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 -2 0 1 1 1
0 -1 0 0 -1 0 0 0
0 -1 0 0 -1 -1 -1 -1
0 -1 0 0 -1 0 -1 0
0 -1 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,-1-t,-1,0,0,0,0)
the Blanchfield form on it
4t^-3-2t^-2-4t^-1+7-4t-2t^2+4t^3
7
First homology
of the double branched cover of 12n_0689
Z/7
-6 6
12n_0690
1

detected by
an unknotting move
1+2t-12t^2+19t^3-12t^4+2t^5+t^6
Seifert matrix of 12n_0690
-1 0 0 -1 1 0
0 -1 0 1 -1 0
-1 0 -1 -1 1 0
0 0 0 1 1 1
0 0 0 1 0 0
0 0 0 1 1 2
1
Generator of the Alexander module
(0,0,t,0,1,1)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
45
First homology
of the double branched cover of 12n_0690
Z/45
0 0
12n_0691
3

detected by
the signature
2-3t-2t^2+12t^3-17t^4+12t^5-2t^6-3t^7+2t^8
Seifert matrix of 12n_0691
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 -2 0 0 1 0
0 -1 0 0 -1 0 0 0
0 -1 0 -1 -1 -1 0 -1
0 -1 0 0 -1 0 -1 0
0 -1 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-4+2t^-3+t^-2-8t^-1+12-8t+t^2+2t^3-t^4
35
First homology
of the double branched cover of 12n_0691
Z/35
-6 6
12n_0692
3

detected by
the signature
2-3t-2t^2+12t^3-17t^4+12t^5-2t^6-3t^7+2t^8
Seifert matrix of 12n_0692
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 -2 0 0 1 1
0 -1 0 0 -1 0 0 0
0 -1 0 -1 -1 -1 0 0
0 -1 0 0 -1 0 -1 0
0 -1 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(2t-6t^2-8t^3-3t^4+6t^5+8t^7+8t^8+2t^9,9t+3t^2+6t^3+6t^4,t^3,3t+2t^3+2t^4,-6t-2t^2-4t^3-4t^4,1+t^3+6t^4+2t^5+4t^6+4t^7+t^8,-t^4-2t^5,-t^4-2t^5)
the Blanchfield form on it
x
35
First homology
of the double branched cover of 12n_0692
Z/35
-6 6
12n_0693
2

detected by
the signature
-1+4t-2t^2-7t^3+13t^4-7t^5-2t^6+4t^7-t^8
Seifert matrix of 12n_0693
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 0 0 0
0 -1 0 1 -1 -1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 0
0 -1 0 1 0 -1 -1 -1
1
Generator of the Alexander module
(0,1+2t,-1-t^2,-2,-2t,2,0,0)
the Blanchfield form on it
-2t^-3+4t^-2+4t^-1-11+4t+4t^2-2t^3
13
First homology
of the double branched cover of 12n_0693
Z/13
-4 4
12n_0694
3

detected by
the signature
1-4t^2+9t^3-11t^4+9t^5-4t^6+t^8
Seifert matrix of 12n_0694
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 -1 0 0 0 0
0 -1 0 1 -1 -1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 0
0 -1 0 1 0 -1 -1 -1
1 or 2
35
First homology
of the double branched cover of 12n_0694
Z/35
-6 6
12n_0695
1

detected by
an unknotting move
1-4t+10t^2-17t^3+21t^4-17t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0695
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 0 0 0
0 -1 0 1 1 -1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 1 1
0 -1 0 1 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+2t^-1-3+2t-t^2
85
First homology
of the double branched cover of 12n_0695
Z/85
0 0
12n_0696
2

detected by
the signature
-1+4t-2t^2-7t^3+13t^4-7t^5-2t^6+4t^7-t^8
Seifert matrix of 12n_0696
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 0 0 0
0 -1 0 1 -1 -1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 -1 -1 -1 0
0 -1 0 1 0 -1 0 -1
1
Generator of the Alexander module
(0,-t,1+t^2,0,t,-1,1+t,t)
the Blanchfield form on it
-t^-3+3t^-2-1+3t^2-t^3
13
First homology
of the double branched cover of 12n_0696
Z/13
-4 4
12n_0697
2

detected by
the signature
1-4t+6t^2-t^3-3t^4-t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0697
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 0 0 1
0 -1 0 1 -1 -1 0 1
0 -1 0 0 0 -1 0 0
0 -1 0 1 0 -1 -1 0
0 0 0 0 0 0 0 1
1 or 2
21
First homology
of the double branched cover of 12n_0697
Z/21
-4 4
12n_0698
2

detected by
the signature
-2+12t-25t^2+31t^3-25t^4+12t^5-2t^6
Seifert matrix of 12n_0698
0 1 0 0 -1 0
0 2 1 0 0 1
-1 2 1 -1 -1 1
-1 1 0 0 -1 0
0 1 0 0 0 0
0 1 0 0 0 2
1
Generator of the Alexander module
(0,0,1,-t,0,0)
the Blanchfield form on it
2t^-2-6t^-1+7-6t+2t^2
109
First homology
of the double branched cover of 12n_0698
Z/109
4 4
12n_0699
1

detected by
an unknotting move
-2+12t-19t^2+12t^3-2t^4
Seifert matrix of 12n_0699
2 1 2 -6
1 2 2 -6
1 2 2 -7
-3 -5 -6 22
1
Generator of the Alexander module
(4-8t-8t^2+22t^3-15t^4+3t^5,-185+403t+370t^2-1067t^3+735t^4-147t^5,-15+33t+30t^2-87t^3+60t^4-12t^5,112-244t-224t^2+646t^3-445t^4+89t^5)
the Blanchfield form on it
72031t^-7-734919t^-6+3018749t^-5-6013758t^-4+3690534t^-3+10321431t^-2-30790852t^-1+40873568-30790852t+10321431t^2+3690534t^3-6013758t^4+3018749t^5-734919t^6+72031t^7
47
First homology
of the double branched cover of 12n_0699
Z/47
2 2
12n_0700
2

detected by
the signature
-2+11t-21t^2+25t^3-21t^4+11t^5-2t^6
Seifert matrix of 12n_0700
1 0 0 0 0 0
0 2 1 0 0 1
0 2 1 0 -1 1
1 0 0 1 0 0
0 1 0 0 0 0
-1 1 0 -1 0 2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-5t^-1+6-5t+2t^2
93
First homology
of the double branched cover of 12n_0700
Z/93
4 4
12n_0701
2

detected by
the Nakanishi index
-3+16t-25t^2+16t^3-3t^4
Seifert matrix of 12n_0701
0 1 0 0
0 2 1 1
-1 2 1 1
0 1 0 3
2
63
First homology
of the double branched cover of 12n_0701
Z/21+Z/3
2 2
12n_0702
1

detected by
an unknotting move
-2+12t-28t^2+37t^3-28t^4+12t^5-2t^6
Seifert matrix of 12n_0702
-1 0 -1 0 0 -1
0 2 0 0 0 0
0 1 0 1 1 0
0 0 1 0 0 1
0 1 0 0 1 0
0 0 0 0 1 -1
1
Generator of the Alexander module
(1,0,-t,0,0,1)
the Blanchfield form on it
2t^-1-3+2t
121
First homology
of the double branched cover of 12n_0702
Z/121
0 0
12n_0703
2

detected by
the signature
1-5t+11t^2-13t^3+13t^4-13t^5+11t^6-5t^7+t^8
Seifert matrix of 12n_0703
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 -1 -1 -1 0 0 -1 0
0 0 0 -1 -1 1 0 0
1 0 0 1 0 -1 0 1
0 -1 -1 0 0 0 -1 0
1 0 -1 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,1-t,-1-t+2t^3-t^4,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+7t^-1-6+7t-4t^2+t^3
73
First homology
of the double branched cover of 12n_0703
Z/73
-4 4
12n_0704
1

detected by
an unknotting move
4-15t+23t^2-15t^3+4t^4
Seifert matrix of 12n_0704
-1 1 1 1
0 7 5 2
0 3 3 1
0 2 2 0
1
Generator of the Alexander module
(-6+8t-2t^2,0,1-t,3-2t)
the Blanchfield form on it
1
61
First homology
of the double branched cover of 12n_0704
Z/61
0 0
12n_0705
1

detected by
an unknotting move
-1+9t-26t^2+37t^3-26t^4+9t^5-t^6
Seifert matrix of 12n_0705
1 0 0 0 0 -1
0 -1 0 0 0 0
0 1 0 0 -1 -1
1 -1 1 1 1 0
0 1 -1 0 -2 -1
0 0 0 0 -1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-1
109
First homology
of the double branched cover of 12n_0705
Z/109
0 0
12n_0706
2

detected by
the Nakanishi index
1-4t+6t^2-8t^3+11t^4-8t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0706
1 0 0 0 0 0 0 0
1 1 0 1 1 0 1 0
-1 0 -1 -1 -1 -1 0 -1
0 0 0 -1 0 0 0 0
1 0 0 0 1 0 0 0
-1 0 0 -1 -1 -1 0 0
1 0 0 1 0 0 1 0
0 0 0 -1 0 0 0 -1
2
49
First homology
of the double branched cover of 12n_0706
Z/7+Z/7
0 0
12n_0707
2

detected by
the signature
-1+4t-11t^2+17t^3-19t^4+17t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0707
0 0 1 0 0 0 1 -1
1 1 1 -1 0 0 1 -1
0 0 1 0 0 0 1 0
0 0 0 0 1 0 0 0
-1 0 -1 1 0 0 -1 1
1 1 1 -1 0 1 1 -1
0 0 0 0 0 0 1 0
0 0 0 -1 1 0 0 0
1 or 2
85
First homology
of the double branched cover of 12n_0707
Z/85
4 4
12n_0708
1

detected by
an unknotting move
1-3t+6t^2-9t^3+11t^4-9t^5+6t^6-3t^7+t^8
Seifert matrix of 12n_0708
0 -1 0 1 0 -1 0 -1
0 -1 0 0 0 0 0 0
-1 0 -1 1 -1 -1 0 0
1 1 0 -2 1 1 0 1
-1 -1 0 1 0 -1 0 -1
0 -1 0 1 0 0 0 -1
-1 0 -1 1 -1 -1 -1 0
0 -1 0 1 0 0 0 0
1
Generator of the Alexander module
(0,0,t+t^2,0,0,1,0,0)
the Blanchfield form on it
t^-3-2t^-2+4t^-1-4+4t-2t^2+t^3
49
First homology
of the double branched cover of 12n_0708
Z/49
0 0
12n_0709
1

detected by
an unknotting move
1-4t+8t^2-11t^3+13t^4-11t^5+8t^6-4t^7+t^8
Seifert matrix of 12n_0709
0 -1 -1 0 -1 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
-1 -1 -1 0 -1 0 -1 0
0 -1 -1 0 0 0 -1 0
-1 0 0 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 0 -2 -1
-1 0 -1 -1 -1 0 -1 0
1
Generator of the Alexander module
(0,2,1,0,0,0,0,0)
the Blanchfield form on it
2t^-3-4t^-2-2t^-1+11-2t-4t^2+2t^3
61
First homology
of the double branched cover of 12n_0709
Z/61
0 2
12n_0710
1

detected by
an unknotting move
2-10t+22t^2-27t^3+22t^4-10t^5+2t^6
Seifert matrix of 12n_0710
1 1 1 0 1 0
0 -1 0 0 0 0
0 -1 -1 0 0 0
1 0 0 -1 -1 -1
1 -1 -1 0 -2 -1
1 0 -1 0 -1 0
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
1
95
First homology
of the double branched cover of 12n_0710
Z/95
-2 2
12n_0711
1

detected by
an unknotting move
1-5t+13t^2-23t^3+29t^4-23t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0711
1 0 1 0 1 -1 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 1 0 0 0
0 -1 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
0 -1 0 -1 0 -1 0 0
1 0 1 -1 1 -1 1 0
-1 1 -1 1 -1 1 -1 -1
1 or 2
113
First homology
of the double branched cover of 12n_0711
Z/113
0 0
12n_0712
2

detected by
the Lickorish test
3-13t+27t^2-33t^3+27t^4-13t^5+3t^6
Seifert matrix of 12n_0712
3 0 3 0 0 0
-1 -3 0 -2 0 0
1 0 2 0 0 0
0 -1 1 -1 0 0
2 1 1 1 1 1
2 1 1 1 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-3t^-2+11t^-1-17+11t-3t^2
119
First homology
of the double branched cover of 12n_0712
Z/119
2 2
12n_0713
2

detected by
the Lickorish test
3-11t+20t^2-23t^3+20t^4-11t^5+3t^6
Seifert matrix of 12n_0713
1 3 3 0 0 2
0 -3 -4 -2 0 -4
0 -6 -6 -3 0 -6
0 -5 -5 -1 0 -4
1 3 3 0 1 2
0 -5 -5 -2 0 -5
1
Generator of the Alexander module
(0,2,0,0,1,1)
the Blanchfield form on it
-3t^-2+8t^-1-12+8t-3t^2
91
First homology
of the double branched cover of 12n_0713
Z/91
2 2
12n_0714
2

detected by
the linking form on L_4
3-14t+30t^2-37t^3+30t^4-14t^5+3t^6
Seifert matrix of 12n_0714
-2 -1 -1 -1 -1 0
-1 1 -1 -1 0 -1
-2 -1 -2 -1 -1 0
0 0 0 -1 0 0
-2 -1 -2 -1 -2 0
0 0 1 0 0 1
2
131
First homology
of the double branched cover of 12n_0714
Z/131
-2 2
12n_0715
1

detected by
an unknotting move
6-22t+33t^2-22t^3+6t^4
Seifert matrix of 12n_0715
-17 -21 -21 -12
-20 -24 -25 -14
-24 -30 -30 -18
-16 -20 -21 -13
1 or 2
89
First homology
of the double branched cover of 12n_0715
Z/89
0 0
12n_0716
1

detected by
an unknotting move
2-9t+18t^2-21t^3+18t^4-9t^5+2t^6
Seifert matrix of 12n_0716
-1 0 0 0 0 0
0 2 0 1 1 0
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
0 0 -1 0 1 0
1 1 1 1 0 -1
1
Generator of the Alexander module
(0,1,0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
79
First homology
of the double branched cover of 12n_0716
Z/79
-2 2
12n_0717
2

detected by
the Lickorish test
1-4t+12t^2-17t^3+12t^4-4t^5+t^6
Seifert matrix of 12n_0717
0 -1 -1 1 0 0
0 1 0 0 0 1
0 0 0 1 0 0
1 1 1 -1 0 0
0 -1 -1 1 1 -1
0 0 -1 1 0 0
2
51
First homology
of the double branched cover of 12n_0717
Z/51
2 2
12n_0718
1

detected by
an unknotting move
2-7t+12t^2-13t^3+12t^4-7t^5+2t^6
Seifert matrix of 12n_0718
0 -1 -1 1 0 0
0 1 0 0 0 1
0 0 0 1 0 0
1 1 1 -2 0 0
0 -1 -1 1 1 -1
0 0 -1 1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-1
55
First homology
of the double branched cover of 12n_0718
Z/55
2 2
12n_0719
1

detected by
an unknotting move
1-5t+13t^2-17t^3+13t^4-5t^5+t^6
Seifert matrix of 12n_0719
0 -1 0 1 -1 1
-1 -1 -1 -1 0 -1
0 0 -1 0 0 0
0 -1 0 0 -1 1
0 0 -1 0 -1 0
0 0 1 0 0 1
1
Generator of the Alexander module
(0,t,0,0,-1,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
55
First homology
of the double branched cover of 12n_0719
Z/55
-2 2
12n_0720
2

detected by
the signature
-2+11t-23t^2+29t^3-23t^4+11t^5-2t^6
Seifert matrix of 12n_0720
-1 0 -1 0 0 0
0 1 1 0 0 0
0 0 -1 0 0 0
0 1 1 -1 0 -1
1 0 1 -1 -2 -1
1 0 1 -1 -1 -2
1
Generator of the Alexander module
(0,-t-3t^2,1+3t,-7t+6t^2,6t-9t^2,1-12t+9t^2)
the Blanchfield form on it
-6t^-2+19t^-1-22+19t-6t^2
101
First homology
of the double branched cover of 12n_0720
Z/101
-4 4
12n_0721
1

detected by
an unknotting move
1-2t+3t^2-4t^3+5t^4-4t^5+3t^6-2t^7+t^8
Seifert matrix of 12n_0721
-1 -1 -1 -1 -1 -1 -1 -1
0 -1 0 -1 -1 -1 -1 -1
0 -1 -1 -1 -1 -1 -1 -1
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+2t^-2-2t^-1+1-2t+2t^2-t^3
25
First homology
of the double branched cover of 12n_0721
Z/25
0 0
12n_0722
3

detected by
the signature
-1+4t-7t^2+10t^3-11t^4+10t^5-7t^6+4t^7-t^8
Seifert matrix of 12n_0722
-1 -1 -1 -1 -1 -1 -1 -1
0 -1 0 -1 -1 -1 -1 -1
0 -1 -1 -1 -1 -1 -1 -1
0 0 0 -2 -2 -1 -2 -2
0 0 0 -1 -2 -1 -1 -2
0 0 0 -1 -1 0 -1 -1
0 0 0 -1 -2 -1 -2 -2
0 0 0 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+4t^-2-6t^-1+7-6t+4t^2-t^3
55
First homology
of the double branched cover of 12n_0722
Z/55
-6 6
12n_0723
1

detected by
an unknotting move
2-4t+3t^2-t^3+3t^4-4t^5+2t^6
Seifert matrix of 12n_0723
-1 -1 -1 -1 1 -1
0 -1 0 -1 1 -1
0 -1 -1 -1 1 -1
0 0 0 0 1 -1
0 0 0 0 1 1
0 0 0 -1 1 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-2t^-2+t^-1+t-2t^2+t^3
19
First homology
of the double branched cover of 12n_0723
Z/19
-2 2
12n_0724
2

detected by
the signature
-2+8t-13t^2+15t^3-13t^4+8t^5-2t^6
Seifert matrix of 12n_0724
-1 -1 -1 -1 1 -1
0 -1 0 -1 1 -1
0 -1 -1 -1 1 -1
0 0 0 -2 2 -1
0 0 0 1 -3 1
0 0 0 -1 1 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-4t^-2+7t^-1-8+7t-4t^2+t^3
61
First homology
of the double branched cover of 12n_0724
Z/61
-4 4
12n_0725
4

detected by
the signature
1-t+t^3-2t^4+3t^5-2t^6+t^7-t^9+t^10
Seifert matrix of 12n_0725
-1 -1 0 -1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0 0 0
0 -1 0 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 0 -1 -1
-1 -1 -1 -1 0 -1 -1 0 0 -1
-1 -1 -1 -1 0 0 -1 0 0 0
0 0 0 0 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 0 -1 -1 0 -1 -1
-1 -1 -1 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-t^-3+t^-1-1+t-t^3+t^4
5
First homology
of the double branched cover of 12n_0725
Z/5
-8 8
12n_0726
2

detected by
the Lickorish test
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 12n_0726
-2 0 0 0
-1 -2 2 -1
1 1 -3 1
-1 -1 1 0
1
Generator of the Alexander module
(0,t,1,t)
the Blanchfield form on it
-2t^-1+4-2t
63
First homology
of the double branched cover of 12n_0726
Z/63
-2 2
12n_0727
1

detected by
an unknotting move
2-10t+21t^2-25t^3+21t^4-10t^5+2t^6
Seifert matrix of 12n_0727
-1 0 0 0 0 0
0 -1 0 1 1 -1
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
0 0 -1 0 1 0
1 0 1 0 -1 2
1
Generator of the Alexander module
(0,-t,0,-1,-1,1)
the Blanchfield form on it
1
91
First homology
of the double branched cover of 12n_0727
Z/91
-2 2
12n_0728
1

detected by
an unknotting move
-1+5t-13t^2+22t^3-25t^4+22t^5-13t^6+5t^7-t^8
Seifert matrix of 12n_0728
-1 0 0 0 -1 0 0 0
1 1 0 1 1 1 0 1
-1 0 -1 0 -1 0 -1 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 0 0 0
1 0 0 1 0 1 0 1
-1 0 0 -1 -1 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-1+1-t
107
First homology
of the double branched cover of 12n_0728
Z/107
-2 2
12n_0729
2

detected by
the signature
-2+9t-16t^2+19t^3-16t^4+9t^5-2t^6
Seifert matrix of 12n_0729
-1 0 0 0 -1 -1
0 0 0 0 1 1
-1 0 -1 -1 -1 -1
0 0 0 -2 -1 -1
0 0 0 0 -1 0
0 1 0 -1 -1 -2
1
Generator of the Alexander module
(0,1,-t,0,0,1)
the Blanchfield form on it
-2t^-2+5t^-1-6+5t-2t^2
73
First homology
of the double branched cover of 12n_0729
Z/73
-4 4
12n_0730
1

detected by
an unknotting move
1-4t+11t^2-15t^3+11t^4-4t^5+t^6
Seifert matrix of 12n_0730
0 0 1 0 1 0
-1 -1 0 -1 0 -1
1 0 0 1 1 0
1 0 1 1 1 0
1 0 1 0 0 0
-1 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
47
First homology
of the double branched cover of 12n_0730
Z/47
-2 2
12n_0731
1

detected by
an unknotting move
-2+11t-28t^2+39t^3-28t^4+11t^5-2t^6
Seifert matrix of 12n_0731
2 0 1 1 1 0
-1 -1 0 -1 0 -1
1 0 2 1 1 0
2 0 1 2 1 0
1 0 1 0 0 0
-1 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,2+4t+11t^2+6t^3,-3-3t-14t^2-24t^3-t^4+6t^5,1+4t^2+3t^3,-3t-3t^2+4t^3+3t^4,3t+7t^2-2t^3+16t^4+4t^5-6t^6)
the Blanchfield form on it
x
121
First homology
of the double branched cover of 12n_0731
Z/121
0 0
12n_0732
1

detected by
an unknotting move
1-9t+28t^2-39t^3+28t^4-9t^5+t^6
Seifert matrix of 12n_0732
-2 0 -2 0 0 -1
0 -1 0 0 0 0
-1 1 -1 0 0 -1
-1 -1 0 1 -1 0
-1 0 -1 0 -1 -1
-1 1 -2 0 0 -2
1
Generator of the Alexander module
(0,2+46t-127t^2+156t^3-92t^4+26t^5,-2-46t+127t^2-156t^3+92t^4-26t^5,1+7t-16t^2-8t^3+42t^4-36t^5+13t^6,0,-2-70t+191t^2-234t^3+138t^4-39t^5)
the Blanchfield form on it
x
115
First homology
of the double branched cover of 12n_0732
Z/115
-2 2
12n_0733
1

detected by
an unknotting move
2-12t+31t^2-41t^3+31t^4-12t^5+2t^6
Seifert matrix of 12n_0733
1 0 1 0 0 0
-1 -1 -1 0 0 -1
0 0 1 0 0 0
0 -1 -1 -1 1 0
1 1 1 0 -2 0
1 0 1 0 0 -1
1
Generator of the Alexander module
(0,t,0,0,1-t,0)
the Blanchfield form on it
2t^-2-9t^-1+16-9t+2t^2
131
First homology
of the double branched cover of 12n_0733
Z/131
-2 2
12n_0734
2

detected by
the signature
-2+10t-19t^2+23t^3-19t^4+10t^5-2t^6
Seifert matrix of 12n_0734
-2 0 0 -1 -1 -1
1 -2 1 0 1 1
-1 1 0 0 -1 -1
-1 -1 0 -2 -1 -1
-2 0 0 -1 -2 -1
-2 0 0 -1 -2 -2
1
Generator of the Alexander module
(0,-2+8t-7t^2+2t^3,1-t,0,0,1+t-3t^2+t^3)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
85
First homology
of the double branched cover of 12n_0734
Z/85
-4 4
12n_0735
1

detected by
an unknotting move
-4+18t-27t^2+18t^3-4t^4
Seifert matrix of 12n_0735
-3 0 0 1
-1 -2 1 0
1 1 0 0
1 -1 0 -2
1
Generator of the Alexander module
(0,3,-2,2)
the Blanchfield form on it
-8t^-1+20-8t
71
First homology
of the double branched cover of 12n_0735
Z/71
-2 2
12n_0736
1

detected by
an unknotting move
2-13t+36t^2-49t^3+36t^4-13t^5+2t^6
Seifert matrix of 12n_0736
2 0 1 1 1 0
-1 -1 -1 -1 0 -1
1 0 2 1 1 1
2 0 1 2 1 0
1 0 1 0 0 0
0 0 0 0 0 1
1
Generator of the Alexander module
(22t-24t^2+20t^3-4t^4,-t,4-4t+5t^2-t^3,t,-1,1+t^2+2t^3)
the Blanchfield form on it
-231t^-6+2610t^-5-13905t^-4+44429t^-3-96297t^-2+150435t^-1-174110+150435t-96297t^2+44429t^3-13905t^4+2610t^5-231t^6
151
First homology
of the double branched cover of 12n_0736
Z/151
2 2
12n_0737
2

detected by
the Nakanishi index
-2+7t-9t^2+9t^3-9t^4+7t^5-2t^6
Seifert matrix of 12n_0737
-2 0 0 0 -1 0
0 0 -1 1 -1 0
-1 0 0 1 -1 0
1 1 1 -2 1 1
-2 0 0 0 -2 0
0 -1 -1 1 0 0
2
45
First homology
of the double branched cover of 12n_0737
Z/15+Z/3
0 2
12n_0738
2

detected by
the signature
-2+13t-30t^2+39t^3-30t^4+13t^5-2t^6
Seifert matrix of 12n_0738
-2 -2 0 -1 1 -1
0 2 0 1 -1 1
1 2 -1 1 -1 1
-1 0 0 -1 0 -1
0 -1 0 -1 0 -1
-1 -1 0 -1 1 -2
1
Generator of the Alexander module
(0,3,t,0,-2,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
129
First homology
of the double branched cover of 12n_0738
Z/129
-4 4
12n_0739
2

detected by
the signature
1-4t+5t^2+t^3-5t^4+t^5+5t^6-4t^7+t^8
Seifert matrix of 12n_0739
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 0 -1 0 0 1
0 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0
1 0 0 1 1 1 1 0
1 0 0 1 1 0 1 0
1 1 0 1 1 1 1 -1
1
Generator of the Alexander module
(4t-2t^2,-6t-15t^2-5t^3-19t^4+25t^5-6t^6,-6t-17t^2-8t^3-15t^4+24t^5-6t^6,8t+6t^2+t^3+17t^4-13t^6+4t^7,-2t+t^2,1-2t+9t^2-4t^3-32t^4-4t^6-18t^7+24t^8-6t^9,12t+34t^2+16t^3+26t^4-54t^5+20t^6-2t^7,-1-14t^2-21t^3-10t^4-48t^5+22t^6-46t^7+49t^8-12t^9)
the Blanchfield form on it
x
13
First homology
of the double branched cover of 12n_0739
Z/13
4 4
12n_0740
1

detected by
an unknotting move
-2+10t-24t^2+33t^3-24t^4+10t^5-2t^6
Seifert matrix of 12n_0740
-2 1 0 -1 0 0
0 1 0 -1 0 0
1 -1 -1 1 0 0
-1 0 0 0 1 -1
0 0 0 0 1 0
-1 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
1
105
First homology
of the double branched cover of 12n_0740
Z/105
0 0
12n_0741
1

detected by
an unknotting move
3-11t+21t^2-25t^3+21t^4-11t^5+3t^6
Seifert matrix of 12n_0741
3 0 3 3 0 3
-1 -3 0 0 -2 0
1 0 2 1 0 1
1 0 2 2 0 2
0 -1 1 1 -1 1
1 0 2 1 0 2
1 or 2
95
First homology
of the double branched cover of 12n_0741
Z/95
2 2
12n_0742
2

detected by
the Lickorish test
2-9t+21t^2-27t^3+21t^4-9t^5+2t^6
Seifert matrix of 12n_0742
-1 0 0 0 0 0
0 2 0 0 0 1
-1 0 0 0 0 -1
0 0 0 1 0 0
-1 -1 -1 0 1 -2
-2 0 -1 1 0 -2
2
91
First homology
of the double branched cover of 12n_0742
Z/91
2 2
12n_0743
2

detected by
the Lickorish test
6-21t+31t^2-21t^3+6t^4
Seifert matrix of 12n_0743
3 0 0 3
-1 -3 -2 0
0 -1 -1 1
1 0 0 3
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
2t^-1-3+2t
85
First homology
of the double branched cover of 12n_0743
Z/85
0 0
12n_0744
2

detected by
the signature
-2+9t-15t^2+17t^3-15t^4+9t^5-2t^6
Seifert matrix of 12n_0744
-1 0 0 0 0 0
0 -1 0 1 0 0
-1 -1 1 -1 1 0
-1 0 0 -1 1 0
1 0 0 0 -2 0
0 -1 0 0 1 -1
1
Generator of the Alexander module
(0,2-4t+3t^2+t^3-t^4,4t-4t^2+t^3,0,1+t-4t^2+t^4,-2t+4t^2-3t^3-t^4+t^5)
the Blanchfield form on it
6t^-2-9t^-1+10-9t+6t^2
69
First homology
of the double branched cover of 12n_0744
Z/69
-4 4
12n_0745
2

detected by
the Nakanishi index
-1+10t-30t^2+43t^3-30t^4+10t^5-t^6
Seifert matrix of 12n_0745
-1 0 0 0 0 0
0 1 0 1 0 0
-1 -1 1 -1 1 0
-1 0 0 -1 1 0
1 0 0 0 1 0
0 -1 0 0 1 -1
2
125
First homology
of the double branched cover of 12n_0745
Z/25+Z/5
0 0
12n_0746
2

detected by
the Lickorish test
2-11t+28t^2-37t^3+28t^4-11t^5+2t^6
Seifert matrix of 12n_0746
-1 0 0 0 0 0
0 2 0 1 0 1
-1 -1 1 -1 1 0
-1 0 0 -1 1 0
1 0 0 0 1 0
0 0 0 0 1 1
2
119
First homology
of the double branched cover of 12n_0746
Z/119
2 2
12n_0747
2

detected by
the signature
-1+5t-13t^2+20t^3-23t^4+20t^5-13t^6+5t^7-t^8
Seifert matrix of 12n_0747
0 0 0 0 0 1 0 0
-1 1 -1 1 0 0 0 1
-1 0 0 0 0 1 0 0
-1 0 -1 0 0 0 0 1
0 0 0 0 1 1 0 0
1 0 1 -1 0 0 0 -1
-1 1 -1 1 0 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+9t^-1-11+9t-4t^2+t^3
101
First homology
of the double branched cover of 12n_0747
Z/101
4 4
12n_0748
1

detected by
an unknotting move
1-4t+9t^2-16t^3+19t^4-16t^5+9t^6-4t^7+t^8
Seifert matrix of 12n_0748
-2 -2 -1 -1 -2 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1
-2 -2 -2 -1 -2 -1 -1 -1
0 -1 0 -1 -1 -1 0 -1
-1 -2 -1 -1 -1 -1 -1 -1
0 0 0 0 0 -1 0 0
-1 -1 -1 -1 -1 -1 0 -1
0 -1 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
-t^-1+1-t
79
First homology
of the double branched cover of 12n_0748
Z/79
-2 2
12n_0749
2

detected by
the Lickorish test
1-t+t^2-t^3+t^4-t^5+t^6
Seifert matrix of 12n_0749
-1 0 0 0 0 1
-1 0 -1 0 0 1
0 1 0 0 0 0
-1 -1 0 -1 1 1
1 1 1 0 -1 -1
1 1 0 0 0 -2
1
Generator of the Alexander module
?
the Blanchfield form on it
?
7
First homology
of the double branched cover of 12n_0749
Z/7
-2 4
12n_0750
2

detected by
the signature
2-5t+7t^2-5t^3+2t^4
Seifert matrix of 12n_0750
-2 -1 -4 -1
-1 -1 -3 -1
-4 -2 -11 -3
0 0 -1 -1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
3t^-1-4+3t
21
First homology
of the double branched cover of 12n_0750
Z/21
-4 4
12n_0751
1

detected by
an unknotting move
1-4t+9t^2-13t^3+15t^4-13t^5+9t^6-4t^7+t^8
Seifert matrix of 12n_0751
-1 0 0 0 0 1 0 0
-1 1 -1 1 0 0 0 1
-1 0 -1 0 0 1 0 0
-1 0 -1 0 0 0 0 1
0 0 0 0 -1 0 0 0
1 0 1 -1 -1 -1 0 -1
-1 1 -1 1 0 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,t-t^2,0,0,0,1,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
69
First homology
of the double branched cover of 12n_0751
Z/69
0 2
12n_0752
2

detected by
the Lickorish test
2-9t+20t^2-25t^3+20t^4-9t^5+2t^6
Seifert matrix of 12n_0752
0 1 1 1 1 1
1 -1 1 1 0 1
0 1 0 1 1 1
2 0 2 1 0 2
1 -1 1 1 -1 1
1 0 1 1 0 2
2
87
First homology
of the double branched cover of 12n_0752
Z/87
-2 2
12n_0753
2

detected by
the signature
-2+11t-24t^2+31t^3-24t^4+11t^5-2t^6
Seifert matrix of 12n_0753
-1 0 0 -1 1 -1
0 -1 -1 0 -1 0
0 0 -2 0 -1 -1
0 0 -1 0 0 -1
0 0 0 1 -2 1
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(0,4-4t+2t^2,0,0,1,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
105
First homology
of the double branched cover of 12n_0753
Z/105
-4 4
12n_0754
1

detected by
an unknotting move
1-5t+13t^2-21t^3+25t^4-21t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0754
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
0 1 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 1 0
-1 0 0 -1 1 1 1 1
0 1 0 -1 0 0 1 0
-1 0 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,-1+2t^3,-1-3t^2,0,-t,1+3t^2,0)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-11+9t-5t^2+t^3
105
First homology
of the double branched cover of 12n_0754
Z/105
0 2
12n_0755
2

detected by
the Lickorish test
1-10t+29t^2-39t^3+29t^4-10t^5+t^6
Seifert matrix of 12n_0755
-2 0 0 -1 -1 -1
0 -1 0 0 0 0
0 1 1 1 0 0
-2 0 0 -2 -1 -1
0 0 0 0 -1 0
-1 1 0 0 -1 0
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
119
First homology
of the double branched cover of 12n_0755
Z/119
-2 2
12n_0756
2

detected by
the Nakanishi index
2-10t+23t^2-29t^3+23t^4-10t^5+2t^6
Seifert matrix of 12n_0756
-1 0 0 0 0 0
0 -1 0 0 0 0
0 1 -1 -1 0 0
-1 0 0 -1 0 0
0 1 0 -1 1 0
1 0 0 1 -1 2
2
99
First homology
of the double branched cover of 12n_0756
Z/33+Z/3
-2 2
12n_0757
2

detected by
the Lickorish test
1-9t+28t^2-39t^3+28t^4-9t^5+t^6
Seifert matrix of 12n_0757
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -1 1 -1 0
0 -1 0 -1 0 0
0 1 -1 1 -2 0
1 0 0 1 -1 -1
2
115
First homology
of the double branched cover of 12n_0757
Z/115
-2 2
12n_0758
3

detected by
the signature
5-14t+21t^2-23t^3+21t^4-14t^5+5t^6
Seifert matrix of 12n_0758
-1 0 -1 0 0 -1
0 -1 0 0 0 0
0 0 -2 1 -1 -1
0 -1 0 -1 0 0
0 1 -1 1 -2 0
0 0 -1 1 -1 -2
1 or 2
103
First homology
of the double branched cover of 12n_0758
Z/103
-6 6
12n_0759
2

detected by
the Lickorish test
-7+28t-41t^2+28t^3-7t^4
Seifert matrix of 12n_0759
-2 0 -1 0
1 -2 0 -1
-1 -1 -2 0
1 -1 0 1
1 or 2
111
First homology
of the double branched cover of 12n_0759
Z/111
-2 2
12n_0760
2

detected by
the Nakanishi index
-2+11t-29t^2+41t^3-29t^4+11t^5-2t^6
Seifert matrix of 12n_0760
-1 0 -1 0 0 -1
-1 1 -1 1 1 0
0 0 -2 0 0 -2
1 0 1 1 0 1
0 0 0 1 1 0
0 0 -1 0 0 -2
2
125
First homology
of the double branched cover of 12n_0760
Z/25+Z/5
0 0
12n_0761
2

detected by
the signature
-1+5t-10t^2+10t^3-9t^4+10t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0761
-1 0 -1 0 0 -1 -1 0
-1 -1 -1 0 0 -1 -1 0
0 0 -1 0 -1 -1 -1 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 0
0 0 0 1 -1 -1 -1 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 -1 0 1
1
Generator of the Alexander module
(0,-2t+3t^3+t^4-6t^5+16t^6-17t^7+13t^8-6t^9+t^10,0,-2-t+t^2-2t^3+10t^4-11t^5+13t^6-7t^7+t^8,2+2t+t^3-8t^4+10t^5-13t^6+7t^7-t^8,-1+t+10t^2-8t^3-19t^4+21t^5-15t^6-t^7+10t^8+4t^9-4t^10,-1-t-3t^2+4t^3+17t^4-18t^5+18t^6-6t^7-4t^8-2t^9+2t^10,-3t+t^2+7t^3-3t^4-4t^5+16t^6-19t^7+12t^8-5t^9+t^10)
the Blanchfield form on it
x
61
First homology
of the double branched cover of 12n_0761
Z/61
-4 4
12n_0762
2

detected by
the signature
-1+5t-10t^2+12t^3-13t^4+12t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0762
-1 0 -1 0 0 -1 -1 0
-1 -1 -1 0 0 -1 -1 0
0 0 -1 0 -1 -1 -1 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 1 -1 -1 -1 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 -1 0 1
1 or 2
69
First homology
of the double branched cover of 12n_0762
Z/69
-4 4
12n_0763
1

detected by
an unknotting move
-1+12t-36t^2+51t^3-36t^4+12t^5-t^6
Seifert matrix of 12n_0763
-1 0 0 0 0 0
0 1 0 1 0 0
0 -1 -1 0 -1 0
-1 0 0 -1 0 0
0 0 0 1 1 1
1 1 0 1 1 2
1 or 2
149
First homology
of the double branched cover of 12n_0763
Z/149
0 0
12n_0764
3

detected by
the signature
3-5t+3t^2-t^3+3t^4-5t^5+3t^6
Seifert matrix of 12n_0764
-1 0 0 0 0 0
0 -1 0 0 0 0
1 0 -2 1 -1 0
0 -1 0 -1 0 0
1 0 -1 1 -2 0
1 -1 0 0 -1 -1
2
23
First homology
of the double branched cover of 12n_0764
Z/23
-6 6
12n_0765
2

detected by
the signature
-3+15t-31t^2+39t^3-31t^4+15t^5-3t^6
Seifert matrix of 12n_0765
-1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 1 -1 0
0 -1 0 -1 0 0
1 0 -1 1 -2 0
1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,-1-t,3-t,-1,1-t,t+t^2)
the Blanchfield form on it
-4t^-2+17t^-1-25+17t-4t^2
137
First homology
of the double branched cover of 12n_0765
Z/137
-4 4
12n_0766
2

detected by
the signature
-3+13t-21t^2+23t^3-21t^4+13t^5-3t^6
Seifert matrix of 12n_0766
1 0 0 0 0 0
0 -1 0 0 0 0
1 0 -2 1 -1 0
0 -1 0 -1 0 0
1 0 -1 1 -2 0
1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,11-7t-2t^2+t^3+2t^4,0,-1,-1+t+t^2)
the Blanchfield form on it
44t^-7-206t^-6+291t^-5-226t^-4+851t^-3-2513t^-2+3927t^-1-4336+3927t-2513t^2+851t^3-226t^4+291t^5-206t^6+44t^7
97
First homology
of the double branched cover of 12n_0766
Z/97
-4 4
12n_0767
1

detected by
an unknotting move
-1+4t-9t^2+15t^3-17t^4+15t^5-9t^6+4t^7-t^8
Seifert matrix of 12n_0767
0 -1 0 0 0 0 -1 0
0 1 0 -1 0 0 0 0
-1 -1 -1 0 0 -1 -1 -1
-1 -1 0 1 1 -1 -1 0
0 0 0 0 1 0 0 0
-1 -1 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
-1 -1 0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,2+t-t^2+t^3,1-t-t^2+t^3-t^4,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
75
First homology
of the double branched cover of 12n_0767
Z/75
2 2
12n_0768
1

detected by
an unknotting move
-1+3t-5t^2+7t^3-5t^4+3t^5-t^6
Seifert matrix of 12n_0768
-1 -1 0 0 0 -1
0 1 0 -1 0 3
-1 -1 -1 0 0 -1
0 -1 0 1 1 -4
0 0 0 0 1 0
0 2 0 -3 -3 13
1
Generator of the Alexander module
(14t-13t^2-25t^3+12t^4-2t^5+t^6,t+2t^2-t^3,-7t-8t^2+24t^3+19t^4-12t^5+2t^6-t^7,1-14t+13t^2+25t^3-12t^4+2t^5-t^6,1+3t+2t^3-t^4,-3+3t+3t^2-2t^3)
the Blanchfield form on it
x
25
First homology
of the double branched cover of 12n_0768
Z/25
0 0
12n_0769
2

detected by
the Lickorish test
2-8t+20t^2-27t^3+20t^4-8t^5+2t^6
Seifert matrix of 12n_0769
1 1 1 0 1 1
0 0 0 0 -1 -1
0 0 1 0 0 0
0 -1 0 -1 -1 -1
1 0 1 0 2 0
0 -1 0 0 0 0
1
Generator of the Alexander module
(2t,0,0,-2t,1+2t-2t^2,0)
the Blanchfield form on it
9t^-3-36t^-2+90t^-1-122+90t-36t^2+9t^3
87
First homology
of the double branched cover of 12n_0769
Z/87
2 2
12n_0770
2

detected by
the signature
-3+16t-35t^2+45t^3-35t^4+16t^5-3t^6
Seifert matrix of 12n_0770
-6 -9 3 -6 0 -3
-5 -5 2 -4 -1 -2
0 1 -1 0 0 0
-4 -6 2 -5 0 -1
-1 -3 1 -2 0 -1
-5 -5 1 -4 -1 -4
1
Generator of the Alexander module
(0,-1+t-5t^2+4t^3-3t^4,1-t+5t^2-4t^3+3t^4,1-t+5t^2-4t^3+3t^4,0,-2+3t-9t^2+9t^3-7t^4+3t^5)
the Blanchfield form on it
896t^-3-4780t^-2+10459t^-1-13448+10459t-4780t^2+896t^3
153
First homology
of the double branched cover of 12n_0770
Z/153
-4 4
12n_0771
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 12n_0771
4 1 2 0 1 0
2 0 1 0 1 0
1 0 1 0 0 0
1 1 0 2 1 1
2 0 1 0 0 0
0 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-6t^-2+15t^-1-20+15t-6t^2+t^3
103
First homology
of the double branched cover of 12n_0771
Z/103
2 2
12n_0772
1

detected by
an unknotting move
3-13t+29t^2-37t^3+29t^4-13t^5+3t^6
Seifert matrix of 12n_0772
1 -1 0 0 0 -1
0 -1 0 0 0 0
0 0 -1 0 0 0
0 1 -1 -2 -1 1
1 0 0 -1 1 0
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+16-12t+5t^2-t^3
127
First homology
of the double branched cover of 12n_0772
Z/127
-2 2
12n_0773
2

detected by
the signature
-3+11t-19t^2+23t^3-19t^4+11t^5-3t^6
Seifert matrix of 12n_0773
1 1 0 0 1 0
-1 2 -1 0 1 0
1 1 1 0 1 0
1 1 1 1 1 1
0 0 0 0 1 0
-1 1 -1 0 1 -1
1 or 2
89
First homology
of the double branched cover of 12n_0773
Z/89
4 4
12n_0774
1

detected by
an unknotting move
-4+13t-17t^2+13t^3-4t^4
Seifert matrix of 12n_0774
0 1 0 0
0 3 1 4
0 0 1 0
-1 3 2 5
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-1-2+t
51
First homology
of the double branched cover of 12n_0774
Z/51
2 2
12n_0775
1

detected by
an unknotting move
1-6t+17t^2-27t^3+29t^4-27t^5+17t^6-6t^7+t^8
Seifert matrix of 12n_0775
-1 -1 0 -1 0 0 0 -1
0 1 0 0 0 0 0 0
-1 0 1 0 0 0 -1 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 0 1 0 0 1 -1 -1
-1 0 0 -1 0 0 -1 -1
0 -1 0 -1 -1 0 0 -1
1 or 2
131
First homology
of the double branched cover of 12n_0775
Z/131
-2 2
12n_0776
1

detected by
an unknotting move
-1+6t-15t^2+21t^3-21t^4+21t^5-15t^6+6t^7-t^8
Seifert matrix of 12n_0776
-1 -1 0 -1 0 0 0 -1
0 -1 0 0 0 0 0 0
-1 0 1 0 0 0 -1 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
-1 0 1 0 0 1 -1 -1
-1 0 0 -1 0 0 -1 -1
0 -1 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,-1-2t-2t^2+2t^3+2t^4,0,0,2t-6t^2+4t^4,-1-2t-2t^2+2t^3+2t^4,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
107
First homology
of the double branched cover of 12n_0776
Z/107
-2 2
12n_0777
1

detected by
an unknotting move
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 12n_0777
-1 1 0 0 -1 0
0 2 0 1 0 1
-1 1 -1 0 -1 0
0 2 0 1 -1 1
0 1 0 0 0 0
0 1 0 0 0 2
1
Generator of the Alexander module
(0,0,1-t+t^2,0,0,-3+3t-2t^2)
the Blanchfield form on it
-1
65
First homology
of the double branched cover of 12n_0777
Z/65
0 2
12n_0778
2

detected by
the signature
-3+11t-18t^2+21t^3-18t^4+11t^5-3t^6
Seifert matrix of 12n_0778
-1 0 -1 -1 0 -1
0 1 0 -1 0 0
0 -1 -1 -1 0 -1
0 -1 0 -2 0 0
0 -1 0 -1 -1 0
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(-7-216t+340t^2+273t^3-548t^4+260t^5,-11-124t+555t^2-352t^3-718t^4+954t^5-380t^6,25+173t-317t^2-260t^3+525t^4-250t^5,6-24t+366t^2-508t^3-403t^4+804t^5-380t^6,-8+32t-90t^2-142t^3+305t^4+216t^5-374t^6+462t^7-374t^8+180t^9,-9+70t-84t^2-65t^3+128t^4-60t^5)
the Blanchfield form on it
x
85
First homology
of the double branched cover of 12n_0778
Z/85
-4 4
12n_0779
2

detected by
the Lickorish test
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 12n_0779
-1 0 0 1 -1 0
0 1 0 0 0 0
0 -1 -1 0 0 0
0 1 0 1 1 0
0 0 1 0 -2 1
0 -1 -1 0 0 -1
2
111
First homology
of the double branched cover of 12n_0779
Z/111
-2 2
12n_0780
1

detected by
an unknotting move
-1+8t-19t^2+25t^3-19t^4+8t^5-t^6
Seifert matrix of 12n_0780
-2 0 -1 -1 -1 0
0 -1 0 0 0 0
-2 0 -1 -1 -2 0
-1 0 -1 0 -1 0
-1 1 -1 -1 -2 0
-1 -1 -1 -1 0 1
1
Generator of the Alexander module
(0,-2+t,0,-2+t,0,3-3t+t^2)
the Blanchfield form on it
-t^-1+2-t
81
First homology
of the double branched cover of 12n_0780
Z/81
0 2
12n_0781
2

detected by
A(F_5)
1-4t+10t^2-19t^3+25t^4-19t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0781
1 0 1 0 1 -1 0 -1
0 -1 0 0 0 0 0 0
0 0 1 0 1 0 0 -1
1 0 1 1 1 -1 0 -1
0 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 -1
0 0 0 0 0 0 0 -1
2
93
First homology
of the double branched cover of 12n_0781
Z/93
0 0
12n_0782
1

detected by
an unknotting move
-2+8t-18t^2+25t^3-18t^4+8t^5-2t^6
Seifert matrix of 12n_0782
1 0 0 0 0 0
-1 0 -1 0 -1 0
1 0 1 0 0 0
1 -1 1 -1 -1 0
0 -2 0 0 -1 0
1 0 1 -1 0 -1
1 or 2
81
First homology
of the double branched cover of 12n_0782
Z/81
0 0
12n_0783
1

detected by
an unknotting move
2-11t+30t^2-41t^3+30t^4-11t^5+2t^6
Seifert matrix of 12n_0783
1 0 1 1 1 0
0 -1 1 1 1 -1
0 0 -2 -1 -1 1
0 0 -1 -2 -1 1
0 0 -2 -1 -2 1
0 0 1 1 0 0
1
Generator of the Alexander module
(24+15t+25t^2-28t^3-18t^4-25t^5+20t^6+4t^7,49+42t+30t^2-42t^3-54t^4-30t^5+56t^6-7t^7,142+117t+125t^2-170t^3-169t^4-127t^5+139t^6+83t^7-39t^8-3t^9,43t+116t^2+58t^3-29t^4-191t^5-61t^6+2t^7+196t^8-76t^9-6t^10,90+81t+74t^2-114t^3-128t^4-76t^5+91t^6+79t^7-39t^8-3t^9,21+18t+13t^2-18t^3-23t^4-13t^5+24t^6-3
the Blanchfield form on it
x
127
First homology
of the double branched cover of 12n_0783
Z/127
-2 2
12n_0784
1

detected by
an unknotting move
1-6t+15t^2-25t^3+29t^4-25t^5+15t^6-6t^7+t^8
Seifert matrix of 12n_0784
-1 0 -1 0 0 0 -1 0
-1 -1 -1 0 0 0 -1 0
0 0 -1 1 -1 1 -1 0
0 0 0 1 0 1 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-3-6t^-2+14t^-1-19+14t-6t^2+t^3
123
First homology
of the double branched cover of 12n_0784
Z/123
-2 2
12n_0785
1

detected by
an unknotting move
-6+23t-33t^2+23t^3-6t^4
Seifert matrix of 12n_0785
1 -1 -1 0
0 -1 -2 0
0 -2 -1 0
1 0 -1 2
1
Generator of the Alexander module
(0,0,8t^2-4t^3,1+4t-18t^2+24t^3-8t^4)
the Blanchfield form on it
-3t^-1+4-3t
91
First homology
of the double branched cover of 12n_0785
Z/91
2 2
12n_0786
1

detected by
an unknotting move
2-12t+33t^2-45t^3+33t^4-12t^5+2t^6
Seifert matrix of 12n_0786
-1 0 0 1 0 0
0 -1 0 -1 0 0
1 -1 1 -1 1 0
0 0 0 -2 0 0
1 -1 0 -1 1 0
1 0 1 -1 1 -1
1
Generator of the Alexander module
(0,0,0,0,2-t,-1+t)
the Blanchfield form on it
3t^-3-18t^-2+51t^-1-70+51t-18t^2+3t^3
139
First homology
of the double branched cover of 12n_0786
Z/139
-2 2
12n_0787
1

detected by
an unknotting move
-1+4t-9t^2+14t^3-15t^4+14t^5-9t^6+4t^7-t^8
Seifert matrix of 12n_0787
1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
1 -1 1 0 0 0 0 0
1 0 1 -1 1 1 1 1
0 -1 0 0 -1 -1 0 -1
0 -1 0 0 0 -1 0 0
1 -1 1 0 0 0 1 0
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1+t,-1,0,-t-t^2,0,0)
the Blanchfield form on it
1
71
First homology
of the double branched cover of 12n_0787
Z/71
-2 2
12n_0788
1

detected by
an unknotting move
-2+10t-25t^2+35t^3-25t^4+10t^5-2t^6
Seifert matrix of 12n_0788
1 0 0 0 0 0
0 -1 0 0 0 0
1 -1 1 0 0 0
1 0 1 -1 1 -1
1 -1 1 0 1 0
0 1 0 0 0 -2
1
Generator of the Alexander module
(0,7-7t+2t^2,-5+2t,14t-14t^2+4t^3,7t-7t^2+2t^3,-7+7t-2t^2)
the Blanchfield form on it
121t^-3-607t^-2+1518t^-1-2128+1518t-607t^2+121t^3
109
First homology
of the double branched cover of 12n_0788
Z/109
0 0
12n_0789
1

detected by
an unknotting move
-2+9t-20t^2+27t^3-20t^4+9t^5-2t^6
Seifert matrix of 12n_0789
-6 0 -4 -2 -4 -3
-2 1 -1 -1 -1 0
-4 0 -2 -1 -2 -2
-2 0 -1 0 -1 -1
-6 0 -4 -2 -5 -2
0 0 0 0 0 -1
1
Generator of the Alexander module
(3+21t-30t^2+32t^3-64t^4+69t^5-64t^6+128t^7-142t^8+80t^9-16t^10,-5-34t+60t^2-130t^3+244t^4-315t^5+371t^6-557t^7+685t^8-695t^9+646t^10-540t^11+318t^12-112t^13+16t^14,-2t^2-13t^3+37t^4-45t^5+55t^6-82t^7+105t^8-128t^9+146t^10-126t^11+64t^12-16t^13,2t^2+13t^3-37t^4+45t^5-55t^6+82t^7-105t^8+128t^9-146t^1
the Blanchfield form on it
x
89
First homology
of the double branched cover of 12n_0789
Z/89
0 0
12n_0790
1

detected by
an unknotting move
1-5t+15t^2-28t^3+35t^4-28t^5+15t^6-5t^7+t^8
Seifert matrix of 12n_0790
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 -1 0 -1 -1 1 1
-1 0 -1 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,-1-t-t^3,-1-t-2t^3,-1-t,0,-2t-t^3,1-t-t^2)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
133
First homology
of the double branched cover of 12n_0790
Z/133
0 0
12n_0791
2

detected by
the signature
1-5t+13t^2-18t^3+19t^4-18t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0791
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 -1 0 -1 -1 1 1
-1 0 -1 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,t-t^2,1,0,0,2,0)
the Blanchfield form on it
-t^-3+3t^-2-4t^-1+4-4t+3t^2-t^3
93
First homology
of the double branched cover of 12n_0791
Z/93
-4 4
12n_0792
1

detected by
an unknotting move
-1+4t-10t^2+16t^3-17t^4+16t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0792
1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
1 -1 1 0 0 0 0 0
1 -1 1 1 0 0 1 0
1 0 1 1 -1 1 1 1
0 -1 0 0 0 -1 0 0
1 -1 1 0 0 0 1 0
1 -1 1 1 0 0 1 1
1
Generator of the Alexander module
(0,2t,1+2t^2-2t^3+2t^4+2t^6,2t-2t^3-2t^5,-3t+3t^2+2t^4-t^5,2t+t^2+t^5,2t,2t+t^3)
the Blanchfield form on it
x
79
First homology
of the double branched cover of 12n_0792
Z/79
2 2
12n_0793
2

detected by
the signature
-3+9t-12t^2+13t^3-12t^4+9t^5-3t^6
Seifert matrix of 12n_0793
-1 -1 -1 -1 1 0
0 -1 0 -1 0 -1
0 -1 -1 -1 0 -1
0 0 0 -1 0 -1
0 0 0 0 1 2
0 0 0 0 2 1
1
Generator of the Alexander module
(-2+6t-2t^2+6t^3+11t^4+2t^5,2-4t+3t^2,-1+2t-2t^2,t,1-2t-2t^3-9t^4-2t^5,-1+4t-2t^3)
the Blanchfield form on it
-22t^-8+27t^-7+313t^-6-850t^-5+1249t^-4-380t^-3-2333t^-2+5311t^-1-6630+5311t-2333t^2-380t^3+1249t^4-850t^5+313t^6+27t^7-22t^8
61
First homology
of the double branched cover of 12n_0793
Z/61
-4 4
12n_0794
1

detected by
an unknotting move
-2+9t-23t^2+33t^3-23t^4+9t^5-2t^6
Seifert matrix of 12n_0794
1 0 0 0 0 0
0 -1 0 0 0 0
1 -1 1 0 0 0
-1 1 -1 2 0 0
1 0 1 -1 -1 1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,-2t+2t^3-2t^4+2t^6,t-5t^2+3t^3+2t^4-4t^5+2t^6+2t^7,1+4t+4t^2-12t^3+11t^4-4t^5-4t^6-2t^7,2t-6t^2+6t^4-6t^5+4t^7,-2t-3t^2+8t^3-6t^4+t^5+4t^6)
the Blanchfield form on it
x
101
First homology
of the double branched cover of 12n_0794
Z/101
0 0
12n_0795
1

detected by
an unknotting move
-6+20t-27t^2+20t^3-6t^4
Seifert matrix of 12n_0795
-1 2 2 1
0 -1 -4 -2
0 -3 -5 -2
0 -2 -3 -2
1
Generator of the Alexander module
(-3+5t-3t^2,-5+3t,0,0)
the Blanchfield form on it
2t^-1-2+2t
79
First homology
of the double branched cover of 12n_0795
Z/79
-2 2
12n_0796
2

detected by
the signature
-2+11t-22t^2+27t^3-22t^4+11t^5-2t^6
Seifert matrix of 12n_0796
-4 -4 0 0 -6 0
-7 -5 -1 0 -9 0
1 0 0 0 0 0
1 0 1 -1 1 0
-9 -8 -1 0 -14 0
1 0 1 -1 1 -1
1 or 2
97
First homology
of the double branched cover of 12n_0796
Z/97
-4 4
12n_0797
1

detected by
an unknotting move
-3+15t-23t^2+15t^3-3t^4
Seifert matrix of 12n_0797
3 0 0 0
2 -5 -2 -5
2 -1 -1 0
1 -5 -1 -7
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
3
59
First homology
of the double branched cover of 12n_0797
Z/59
-2 2
12n_0798
2

detected by
A(F_2)
1-7t+22t^2-31t^3+22t^4-7t^5+t^6
Seifert matrix of 12n_0798
-1 0 0 0 1 0
0 1 0 0 0 0
1 0 1 1 -1 1
0 -1 0 -1 0 0
0 1 0 0 1 0
1 -1 0 0 -1 1
2
91
First homology
of the double branched cover of 12n_0798
Z/91
2 2
12n_0799
1

detected by
an unknotting move
2-13t+32t^2-41t^3+32t^4-13t^5+2t^6
Seifert matrix of 12n_0799
-2 -4 0 -2 0 2
-2 -1 0 -1 -1 1
1 2 -1 2 0 -1
-2 -4 0 -1 0 2
0 -2 0 -1 0 1
0 1 0 0 0 -1
1
Generator of the Alexander module
(2t+16t^2-72t^3+64t^4-46t^5+12t^6,-12-24t+44t^2+126t^3-73t^4-92t^5+116t^6-92t^7+24t^8,1+8t-36t^2+32t^3-23t^4+6t^5,-6-13t+46t^2+18t^3-32t^4+23t^5-6t^6,-3-8t+11t^2+63t^3-64t^4+46t^5-12t^6,-6-13t+46t^2+18t^3-32t^4+23t^5-6t^6)
the Blanchfield form on it
x
135
First homology
of the double branched cover of 12n_0799
Z/135
-2 2
12n_0800
1

detected by
an unknotting move
-1+5t-13t^2+24t^3-29t^4+24t^5-13t^6+5t^7-t^8
Seifert matrix of 12n_0800
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 0 -1 -1 -1 0
0 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 0 -1 -1 -1 -1 0
1 0 0 1 1 0 0 1
1
Generator of the Alexander module
(0,0,0,-t,0,0,1+t,-1-t)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
115
First homology
of the double branched cover of 12n_0800
Z/115
2 2
12n_0801
1

detected by
an unknotting move
-1+5t-7t^2+5t^3-t^4
Seifert matrix of 12n_0801
1 2 0 2
1 1 0 1
-1 -2 -2 -3
1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-1-1+t
19
First homology
of the double branched cover of 12n_0801
Z/19
-2 2
12n_0802
1

detected by
an unknotting move
1-5t+14t^2-25t^3+31t^4-25t^5+14t^6-5t^7+t^8
Seifert matrix of 12n_0802
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 1 0 0 0 -1
-1 -1 -1 0 1 -1 0 -1
0 -1 0 0 0 -1 0 0
-1 -1 -1 1 0 -1 1 -1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
-t^-1+1-t
121
First homology
of the double branched cover of 12n_0802
Z/121
0 0
12n_0803
2

detected by
the signature
1-5t+14t^2-21t^3+23t^4-21t^5+14t^6-5t^7+t^8
Seifert matrix of 12n_0803
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 1 0 0 0 -1
-1 -1 -1 0 -1 -1 0 -1
0 -1 0 0 0 -1 0 0
-1 -1 -1 1 0 -1 1 -1
0 0 0 0 0 0 0 -1
1 or 2
105
First homology
of the double branched cover of 12n_0803
Z/105
-4 4
12n_0804
1

detected by
an unknotting move
1-4t+11t^2-20t^3+23t^4-20t^5+11t^6-4t^7+t^8
Seifert matrix of 12n_0804
-1 0 0 0 0 0 0 0
1 1 0 1 1 1 1 1
-1 0 -1 0 -1 -1 0 -1
0 0 0 1 1 1 0 1
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
1 0 0 1 1 1 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(192-396t-458t^2+570t^3-96t^4+668t^5+960t^6,-141+377t+468t^2-1091t^3-541t^4-262t^5-1043t^6+698t^7+960t^8,7-86t-54t^2+475t^3+380t^4+49t^5+307t^6-349t^7-480t^8,76-128t-198t^2+128t^3-104t^4+144t^5+288t^6,62-106t-160t^2+111t^3-80t^4+125t^5+240t^6,12-6t-39t^2-27t^3-48t^4-36t^5,-3+36t+129t^2-39t^3-973t^4-
the Blanchfield form on it
x
95
First homology
of the double branched cover of 12n_0804
Z/95
-2 2
12n_0805
2

detected by
the Lickorish test
-2+8t-19t^2+27t^3-19t^4+8t^5-2t^6
Seifert matrix of 12n_0805
-1 0 0 0 0 0
1 1 0 1 1 -1
-1 0 -1 0 0 1
0 0 0 1 0 -1
1 0 0 1 1 -1
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,1,t-t^2,-t,0)
the Blanchfield form on it
2t^-2-6t^-1+7-6t+2t^2
85
First homology
of the double branched cover of 12n_0805
Z/85
0 0
12n_0806
3

detected by
the signature
4-10t+12t^2-11t^3+12t^4-10t^5+4t^6
Seifert matrix of 12n_0806
-1 1 -1 1 -1 1
0 -2 0 -1 0 -1
0 0 -1 1 -1 1
0 -1 0 -2 0 -1
0 0 0 0 -1 1
0 -1 0 -1 0 -2
2
63
First homology
of the double branched cover of 12n_0806
Z/21+Z/3
-6 6
12n_0807
2

detected by
the signature
-2+8t-12t^2+13t^3-12t^4+8t^5-2t^6
Seifert matrix of 12n_0807
-1 1 -1 1 -1 1
0 -2 0 -1 0 -1
0 0 -1 1 -1 1
0 -1 0 0 0 -1
0 0 0 0 -1 1
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,0,2t)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
57
First homology
of the double branched cover of 12n_0807
Z/57
-4 4
12n_0808
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 12n_0808
-1 -1 -1 -1
-1 -1 -2 -3
-1 -1 -3 -3
-2 -3 -4 -4
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-t^-1+2-t
31
First homology
of the double branched cover of 12n_0808
Z/31
-2 2
12n_0809
1

detected by
an unknotting move
-2+4t-3t^2+4t^3-2t^4
Seifert matrix of 12n_0809
-1 -1 1 -1
-1 -1 0 -1
-1 -1 -1 1
0 -1 0 -2
1
Generator of the Alexander module
(1,0,1-2t,0)
the Blanchfield form on it
-t^-1+2-t
15
First homology
of the double branched cover of 12n_0809
Z/15
-2 2
12n_0810
2

detected by
the Lickorish test
2-8t+12t^2-11t^3+12t^4-8t^5+2t^6
Seifert matrix of 12n_0810
-1 1 -1 1 -1 1
0 0 0 -1 0 -1
0 0 -1 1 -1 1
0 -1 0 0 0 -1
0 0 0 0 -1 1
0 -1 0 -1 0 0
1
Generator of the Alexander module
(0,0,-t^2,0,1+t^2-t^3,0)
the Blanchfield form on it
-3t^-5+18t^-4-52t^-3+99t^-2-140t^-1+154-140t+99t^2-52t^3+18t^4-3t^5
55
First homology
of the double branched cover of 12n_0810
Z/55
-2 2
12n_0811
1

detected by
an unknotting move
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 12n_0811
-1 1 -1 1 0 1
0 -2 0 -1 0 -1
0 0 -1 0 -1 1
0 -1 0 0 1 -1
0 0 0 0 1 0
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(t,0,-2,1,0,0)
the Blanchfield form on it
2t^-2-5t^-1+8-5t+2t^2
63
First homology
of the double branched cover of 12n_0811
Z/63
-2 2
12n_0812
1

detected by
an unknotting move
1-2t+3t^2-2t^3+t^4
Seifert matrix of 12n_0812
-3 -3 -4 -3
-4 -4 -6 -5
-4 -4 -5 -4
-4 -5 -5 -4
1
Generator of the Alexander module
(0,t,1,-t)
the Blanchfield form on it
-3t^-1+4-3t
9
First homology
of the double branched cover of 12n_0812
Z/9
0 0
12n_0813
2

detected by
the Nakanishi index
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0813
-1 1 -1 1 0 1
0 0 0 -1 0 -1
0 0 -1 0 -1 1
0 -1 0 0 1 -1
0 0 0 0 1 0
0 -1 0 -1 0 0
2
81
First homology
of the double branched cover of 12n_0813
Z/9+Z/9
0 0
12n_0814
2

detected by
the Lickorish test
-6+24t-35t^2+24t^3-6t^4
Seifert matrix of 12n_0814
0 -1 -1 0
-2 0 1 -1
-2 1 0 -1
-1 0 -1 -2
1
Generator of the Alexander module
(0,2,2,1)
the Blanchfield form on it
-2t^-1+4-2t
95
First homology
of the double branched cover of 12n_0814
Z/95
-2 2
12n_0815
1

detected by
an unknotting move
-1+2t-t^2+2t^3-t^4
Seifert matrix of 12n_0815
-1 1 -2 1
0 0 0 1
0 0 -1 0
0 1 -1 2
1
Generator of the Alexander module
(1,0,0,1)
the Blanchfield form on it
-t^-1+2-t
7
First homology
of the double branched cover of 12n_0815
Z/7
-2 2
12n_0816
1

detected by
an unknotting move
-2+11t-26t^2+35t^3-26t^4+11t^5-2t^6
Seifert matrix of 12n_0816
-1 1 -1 1 0 1
0 2 0 1 0 1
0 0 -1 0 -1 1
0 1 0 2 1 1
0 0 0 0 1 0
0 1 0 1 0 0
1
Generator of the Alexander module
(2+2t-6t^2+4t^3,0,2t-5t^2+2t^3,0,1-2t,-1+t+2t^2)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
113
First homology
of the double branched cover of 12n_0816
Z/113
0 0
12n_0817
2

detected by
the Nakanishi index
-2+6t-10t^2+13t^3-10t^4+6t^5-2t^6
Seifert matrix of 12n_0817
1 0 0 0 -1 0
0 1 2 0 2 0
0 2 1 0 2 0
0 -1 0 -1 0 -1
0 1 1 0 2 0
0 0 1 0 1 -1
2
49
First homology
of the double branched cover of 12n_0817
Z/7+Z/7
0 0
12n_0818
1

detected by
an unknotting move
1-9t+22t^2-27t^3+22t^4-9t^5+t^6
Seifert matrix of 12n_0818
1 0 0 0 0 0
1 -1 0 0 1 0
-1 0 -1 0 -1 0
0 -1 0 -1 1 -1
-1 0 0 0 1 0
1 -1 0 0 1 -1
1 or 2
91
First homology
of the double branched cover of 12n_0818
Z/91
-2 2
12n_0819
1

detected by
an unknotting move
3-12t+24t^2-29t^3+24t^4-12t^5+3t^6
Seifert matrix of 12n_0819
3 3 4 2 4 3
2 1 2 1 2 2
3 3 3 2 4 3
3 3 3 1 2 3
4 4 4 1 3 4
2 1 2 1 2 1
1 or 2
107
First homology
of the double branched cover of 12n_0819
Z/107
-2 2
12n_0820
3

detected by
the signature
1-6t+12t^2-17t^3+19t^4-17t^5+12t^6-6t^7+t^8
Seifert matrix of 12n_0820
0 0 0 -1 0 0 0 0
-1 1 -1 0 1 0 1 0
-1 0 0 -1 0 0 0 0
-1 0 -1 0 0 0 1 0
-1 0 -1 0 1 0 1 0
-1 1 -1 0 1 1 1 0
0 0 0 0 0 0 1 0
0 0 0 1 0 0 0 1
1 or 2
91
First homology
of the double branched cover of 12n_0820
Z/91
6 6
12n_0821
1

detected by
an unknotting move
-1+3t-5t^2+6t^3-5t^4+6t^5-5t^6+3t^7-t^8
Seifert matrix of 12n_0821
0 0 0 -1 0 0 0 0
-1 0 -1 -1 0 -1 0 0
-1 0 0 -1 0 0 0 0
-1 -1 -1 -2 -1 -1 0 -1
-1 -1 -1 -1 0 -1 0 0
-1 0 -1 -1 0 0 0 0
0 -1 0 -1 -1 -1 -1 0
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,-t,0,1,1,0,-t,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
35
First homology
of the double branched cover of 12n_0821
Z/35
2 2
12n_0822
1

detected by
an unknotting move
1-3t+6t^2-11t^3+13t^4-11t^5+6t^6-3t^7+t^8
Seifert matrix of 12n_0822
-2 -2 -1 -1 -1 -1 -2 -1
-1 -1 -1 -1 -1 -1 -1 -1
-2 -2 -2 -1 -1 -1 -2 -1
0 -1 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 0
-1 -1 -1 -1 -1 0 -1 -1
-1 -2 -1 -1 -1 -1 -1 -1
0 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(-t,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-1-2+t
55
First homology
of the double branched cover of 12n_0822
Z/55
-2 2
12n_0823
2

detected by
the signature
-2+12t-24t^2+29t^3-24t^4+12t^5-2t^6
Seifert matrix of 12n_0823
0 0 0 -1 3 0
0 1 0 0 0 0
-1 0 0 -1 3 0
-1 1 -1 0 0 1
2 -3 2 0 2 -2
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,t-t^2,1,-2-4t+2t^2,0)
the Blanchfield form on it
-27t^-3+163t^-2-329t^-1+398-329t+163t^2-27t^3
105
First homology
of the double branched cover of 12n_0823
Z/105
4 4
12n_0824
1

detected by
an unknotting move
-2+7t-14t^2+19t^3-14t^4+7t^5-2t^6
Seifert matrix of 12n_0824
0 0 0 -1 3 0
0 -1 0 -1 3 0
-1 0 0 -1 3 0
-1 0 -1 -2 5 0
2 0 2 5 -11 0
0 0 0 -1 2 -1
1
Generator of the Alexander module
(0,-2+t-t^2+t^3,2-2t+2t^2-t^3,0,1,0)
the Blanchfield form on it
t^-1-2+t
65
First homology
of the double branched cover of 12n_0824
Z/65
0 0
12n_0825
1

detected by
an unknotting move
-2+6t-9t^2+11t^3-9t^4+6t^5-2t^6
Seifert matrix of 12n_0825
0 1 1 1 1 1
0 1 0 0 0 0
0 1 0 1 1 1
1 1 1 0 0 1
0 1 0 0 -2 0
0 1 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-1+2-t
45
First homology
of the double branched cover of 12n_0825
Z/45
0 2
12n_0826
1

detected by
an unknotting move
1-9t+24t^2-31t^3+24t^4-9t^5+t^6
Seifert matrix of 12n_0826
-1 0 -1 0 -1 -1
0 1 0 0 0 0
0 -1 -1 0 -1 -1
0 1 0 -2 0 -1
0 0 0 -1 0 -1
0 0 0 -1 -1 -2
1
Generator of the Alexander module
(-1-t+t^2,0,1-3t^2+t^3,-1-t+t^2,0,0)
the Blanchfield form on it
t^-2-7t^-1+9-7t+t^2
99
First homology
of the double branched cover of 12n_0826
Z/99
-2 2
12n_0827
2

detected by
the Lickorish test
-1+5t-14t^2+25t^3-29t^4+25t^5-14t^6+5t^7-t^8
Seifert matrix of 12n_0827
-1 0 0 0 -1 0 0 -1
1 1 0 1 1 1 1 1
-1 0 -1 0 -1 -1 0 -1
0 0 0 1 0 1 0 0
0 0 0 0 -1 0 0 -1
0 0 0 0 0 -1 0 0
1 0 0 1 0 1 1 0
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,-t,t,1,0,0,1,0)
the Blanchfield form on it
t^-3-5t^-2+10t^-1-12+10t-5t^2+t^3
119
First homology
of the double branched cover of 12n_0827
Z/119
-2 2
12n_0828
1

detected by
an unknotting move
-3+12t-24t^2+31t^3-24t^4+12t^5-3t^6
Seifert matrix of 12n_0828
1 1 1 0 0 0
0 1 2 0 0 0
0 2 1 0 0 0
0 -1 0 -1 0 -1
1 1 1 0 1 0
-1 -1 0 0 0 -1
1
Generator of the Alexander module
(0,1-t,0,-t+t^2,t,1-t)
the Blanchfield form on it
-3t^-1+6-3t
109
First homology
of the double branched cover of 12n_0828
Z/109
0 0
12n_0829
1

detected by
an unknotting move
1-5t+11t^2-18t^3+21t^4-18t^5+11t^6-5t^7+t^8
Seifert matrix of 12n_0829
0 0 0 0 -1 0 0 0
0 1 0 0 0 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 -1 0 0 0 1 0
-1 1 -1 1 0 0 1 1
-1 0 -1 1 0 1 1 1
0 0 0 0 0 0 1 0
-1 0 -1 1 0 0 1 0
1
Generator of the Alexander module
(0,0,0,0,1+t+t^2,1+t^2,0,0)
the Blanchfield form on it
-t^-3+4t^-2-5t^-1+5-5t+4t^2-t^3
91
First homology
of the double branched cover of 12n_0829
Z/91
2 2
12n_0830
2

detected by
the signature
2-4t+5t^2-4t^3+2t^4
Seifert matrix of 12n_0830
-2 -3 0 -1
-3 -6 -1 -2
-1 -3 -2 -1
0 -1 0 -1
1
Generator of the Alexander module
(0,1,2,0)
the Blanchfield form on it
2t^-1-2+2t
17
First homology
of the double branched cover of 12n_0830
Z/17
-4 4
12n_0831
1

detected by
an unknotting move
-1+5t-12t^2+20t^3-23t^4+20t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0831
-1 0 0 0 -1 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 -1 0 0 0
-1 0 -1 0 0 0 1 0
-1 0 -1 1 -1 0 1 1
-1 0 -1 1 0 1 1 1
0 0 0 0 0 0 1 0
-1 0 -1 1 0 0 1 0
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
1
99
First homology
of the double branched cover of 12n_0831
Z/99
-2 2
12n_0832
2

detected by
the signature
-3+13t-23t^2+27t^3-23t^4+13t^5-3t^6
Seifert matrix of 12n_0832
2 1 0 0 0 1
3 3 0 0 0 3
1 0 -1 0 0 0
-1 -2 -1 1 0 -2
1 1 0 0 1 1
3 2 0 0 0 3
1 or 2
105
First homology
of the double branched cover of 12n_0832
Z/105
4 4
12n_0833
1

detected by
an unknotting move
3-11t+22t^2-27t^3+22t^4-11t^5+3t^6
Seifert matrix of 12n_0833
-2 -3 -2 0 0 -2
-1 -3 -1 0 0 -1
-1 -1 0 0 0 0
1 2 1 1 1 0
0 0 0 0 1 0
-2 -2 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-3t^-2+9t^-1-13+9t-3t^2
99
First homology
of the double branched cover of 12n_0833
Z/99
2 2
12n_0834
2

detected by
the signature
-2+12t-26t^2+33t^3-26t^4+12t^5-2t^6
Seifert matrix of 12n_0834
1 0 0 0 0 0
0 -1 0 -1 0 -1
1 0 -1 -1 0 -1
0 0 -1 -2 0 -1
1 0 0 -1 -1 -1
0 0 0 -1 0 -2
1
Generator of the Alexander module
(0,-t,0,1,0,1)
the Blanchfield form on it
-2t^-2+11t^-1-17+11t-2t^2
113
First homology
of the double branched cover of 12n_0834
Z/113
-4 4
12n_0835
1

detected by
an unknotting move
1-4t^2+7t^3-4t^4+t^6
Seifert matrix of 12n_0835
-1 0 -1 0 -1 0
0 -1 0 -1 0 -1
0 0 0 0 -1 -1
0 0 0 0 0 -1
0 0 -1 -1 0 -1
0 0 0 -1 0 0
1
Generator of the Alexander module
(t,-t,0,1,t,0)
the Blanchfield form on it
t^-2+t^-1-3+t+t^2
13
First homology
of the double branched cover of 12n_0835
Z/13
0 2
12n_0836
2

detected by
the signature
-2+12t-27t^2+35t^3-27t^4+12t^5-2t^6
Seifert matrix of 12n_0836
-1 0 -1 0 -1 0
0 -1 0 -1 0 -1
0 0 -2 -1 -1 -1
0 0 -1 -2 0 -1
0 0 -1 -1 0 -1
0 0 0 -1 0 -2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
117
First homology
of the double branched cover of 12n_0836
Z/117
-4 4
12n_0837
2

detected by
the Nakanishi index
1-7t+21t^2-35t^3+41t^4-35t^5+21t^6-7t^7+t^8
Seifert matrix of 12n_0837
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 -1 -1 0
-1 0 1 0 0 0 0 0
0 0 0 1 0 1 0 0
0 -1 0 0 -1 0 -1 0
0 0 0 0 0 1 0 0
0 0 0 -1 0 -1 -1 0
-1 0 1 0 -1 0 0 1
2
169
First homology
of the double branched cover of 12n_0837
Z/13+Z/13
0 2
12n_0838
2

detected by
the Nakanishi index
1-6t+11t^2-6t^3+t^4
Seifert matrix of 12n_0838
1 0 1 -1
1 0 1 0
0 1 -2 0
-2 0 -1 0
2
25
First homology
of the double branched cover of 12n_0838
Z/5+Z/5
0 0
12n_0839
2

detected by
the Nakanishi index
1-7t+18t^2-23t^3+23t^4-23t^5+18t^6-7t^7+t^8
Seifert matrix of 12n_0839
-1 -1 0 0 -1 0 0 0
0 1 0 0 0 -1 0 0
-1 0 1 0 0 0 0 0
0 0 0 1 0 1 0 0
0 -1 0 0 -1 0 -1 0
0 0 0 0 0 1 0 0
0 1 0 -1 0 -1 1 0
-1 0 1 0 -1 0 0 1
2
121
First homology
of the double branched cover of 12n_0839
Z/11+Z/11
4 4
12n_0840
2

detected by
A(F_2)
-1+6t-16t^2+24t^3-25t^4+24t^5-16t^6+6t^7-t^8
Seifert matrix of 12n_0840
-1 -1 0 0 0 -1 0 0
0 1 0 0 0 0 -1 0
-1 0 1 -1 0 0 0 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 1 0 1 0
0 -1 0 0 0 -1 0 -1
0 0 0 0 0 0 1 0
0 1 0 0 -1 0 -1 1
2
119
First homology
of the double branched cover of 12n_0840
Z/119
2 2
12n_0841
1

detected by
an unknotting move
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0841
-1 0 0 1 0 0
-1 0 -1 1 1 0
-1 -1 0 0 0 -1
0 1 0 2 2 1
0 1 0 1 2 1
-1 1 -1 1 1 0
1
Generator of the Alexander module
(0,0,0,2,1,1+t-t^2)
the Blanchfield form on it
2t^-2-6t^-1+7-6t+2t^2
81
First homology
of the double branched cover of 12n_0841
Z/81
0 0
12n_0842
1

detected by
an unknotting move
1-7t+21t^2-38t^3+47t^4-38t^5+21t^6-7t^7+t^8
Seifert matrix of 12n_0842
1 0 1 -1 0 0 0 1
-1 -1 -1 0 0 -1 0 -1
0 0 1 -1 -1 0 -1 1
0 0 0 -1 0 0 0 0
0 0 0 -1 -1 0 0 0
-1 0 -1 0 0 -1 0 0
0 0 0 0 0 0 1 0
0 0 0 -1 -1 0 -1 1
1
Generator of the Alexander module
(0,-2-37t+105t^2-113t^3+104t^4-46t^5+12t^6-2t^7,0,1-t+19t^2-15t^3+10t^5-6t^6+t^7,-1+3t-t^2,-1-5t+3t^2-7t^3+16t^4-14t^5+6t^6-t^7,0,6t^2-22t^3+22t^4-16t^5+4t^6)
the Blanchfield form on it
x
181
First homology
of the double branched cover of 12n_0842
Z/181
0 0
12n_0843
2

detected by
the Nakanishi index
3-15t+34t^2-43t^3+34t^4-15t^5+3t^6
Seifert matrix of 12n_0843
-1 -1 0 0 0 0
0 1 0 0 1 0
-1 -1 -1 0 -1 0
1 0 0 -2 0 -1
0 0 0 0 1 0
1 0 1 -1 0 -2
2
147
First homology
of the double branched cover of 12n_0843
Z/21+Z/7
-2 2
12n_0844
2

detected by
the Nakanishi index
3-12t+16t^2-13t^3+16t^4-12t^5+3t^6
Seifert matrix of 12n_0844
1 -1 1 0 0 0
0 1 0 0 1 0
0 -1 1 0 -1 0
1 0 0 -2 0 -1
0 0 0 0 1 0
1 0 1 -1 0 -2
2
75
First homology
of the double branched cover of 12n_0844
Z/15+Z/5
2 2
12n_0845
2

detected by
the Lickorish test
3-12t+22t^2-25t^3+22t^4-12t^5+3t^6
Seifert matrix of 12n_0845
-9 -3 -3 -6 -6 -6
0 -1 0 0 0 0
-6 -2 -3 -4 -4 -3
-7 -2 -2 -4 -4 -4
-8 -2 -3 -5 -5 -4
-4 -1 -1 -3 -2 -2
1 or 2
99
First homology
of the double branched cover of 12n_0845
Z/99
-2 2
12n_0846
2

detected by
the Nakanishi index
5-20t+31t^2-20t^3+5t^4
Seifert matrix of 12n_0846
-25 -25 -15 -10
-21 -20 -12 -8
-14 -14 -8 -5
-11 -11 -6 -4
2
81
First homology
of the double branched cover of 12n_0846
Z/9+Z/9
0 0
12n_0847
2

detected by
the Nakanishi index
1-7t+18t^2-23t^3+18t^4-7t^5+t^6
Seifert matrix of 12n_0847
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 1
-1 -1 0 -1 0 0
0 -1 0 0 1 0
0 0 0 -1 -1 -1
2
75
First homology
of the double branched cover of 12n_0847
Z/15+Z/5
-2 2
12n_0848
2

detected by
the signature
-1+5t-12t^2+16t^3-17t^4+16t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0848
1 0 0 1 0 0 0 0
-1 -1 -1 -1 -1 0 -1 0
-1 0 -1 -1 -1 0 0 0
0 0 0 1 0 0 0 0
1 0 0 1 -1 0 0 -1
0 -1 -1 -1 0 -1 -1 0
-1 0 -1 -1 -1 0 -1 0
1 0 0 1 0 0 0 -1
2
85
First homology
of the double branched cover of 12n_0848
Z/85
-4 4
12n_0849
2

detected by
the signature
-3+17t-37t^2+47t^3-37t^4+17t^5-3t^6
Seifert matrix of 12n_0849
-2 0 0 1 0 0
-1 -2 -1 0 -1 -2
0 0 -1 0 0 0
1 -1 -1 -2 -1 -1
-1 -1 0 0 0 -1
-1 -1 -1 0 -1 -2
1
Generator of the Alexander module
(0,0,-5+24t-46t^2+54t^3-30t^4+6t^5,6-13t+24t^2-21t^3+6t^4,-7+32t-76t^2+103t^3-84t^4+36t^5-6t^6,7t-32t^2+76t^3-103t^4+84t^5-36t^6+6t^7)
the Blanchfield form on it
-214564t^-4+1471065t^-3-4310496t^-2+7734980t^-1-9304514+7734980t-4310496t^2+1471065t^3-214564t^4
161
First homology
of the double branched cover of 12n_0849
Z/161
-4 4
12n_0850
3

detected by
the signature
1-2t^2+4t^3-5t^4+4t^5-2t^6+t^8
Seifert matrix of 12n_0850
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 0 -1 0 0 -1 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 -1 0 0 0 -1 0 0
0 0 0 0 -1 0 -1 -1
1 -1 0 0 0 0 0 -1
1 or 2
15
First homology
of the double branched cover of 12n_0850
Z/15
-6 6
12n_0851
2

detected by
the signature
2-t-3t^2+5t^3-3t^4-t^5+2t^6
Seifert matrix of 12n_0851
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 0 -1 -1 0 0
0 -1 0 -1 0 0
0 0 0 0 -2 0
1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,-1,1,t,0,1)
the Blanchfield form on it
2t^-2+t^-1-5+t+2t^2
5
First homology
of the double branched cover of 12n_0851
Z/5
-4 4
12n_0852
1

detected by
an unknotting move
1-5t+14t^2-26t^3+33t^4-26t^5+14t^6-5t^7+t^8
Seifert matrix of 12n_0852
-1 0 0 0 0 0 0 0
0 1 1 0 -1 0 1 0
0 0 -1 0 0 0 0 0
0 0 1 -1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 1 0 0 -1 1 1 1
0 0 1 0 -1 0 1 0
0 1 1 0 -1 0 1 1
1
Generator of the Alexander module
(0,-1+t-2t^2+t^3,0,2t-t^2,0,1+t-t^2,0,0)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
125
First homology
of the double branched cover of 12n_0852
Z/125
0 0
12n_0853
1

detected by
an unknotting move
-3+13t-28t^2+37t^3-28t^4+13t^5-3t^6
Seifert matrix of 12n_0853
0 1 0 -1 -2 0
1 1 0 1 0 0
0 -1 -1 0 1 -1
0 1 0 0 -2 0
-1 1 0 -1 -1 0
0 -1 0 0 1 -1
1
Generator of the Alexander module
(1-10t-37t^2-5t^3+58t^4-t^5+10t^6-6t^7,0,-22-50t+52t^2-2t^3-4t^4+4t^5,-9-21t+20t^2-t^3-2t^4+2t^5,52+101t-171t^2+22t^3+3t^4-6t^5+2t^6,-26-55t+74t^2-t^3-2t^4+2t^5)
the Blanchfield form on it
x
125
First homology
of the double branched cover of 12n_0853
Z/125
0 0
12n_0854
1

detected by
an unknotting move
3-14t+33t^2-43t^3+33t^4-14t^5+3t^6
Seifert matrix of 12n_0854
-2 0 0 -1 0 0
1 -1 -1 0 0 0
1 0 -1 1 0 0
-1 0 0 -2 0 0
1 0 -1 1 1 1
1 0 -1 0 0 1
1
Generator of the Alexander module
(0,-t,0,1,-t,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
143
First homology
of the double branched cover of 12n_0854
Z/143
-2 2
12n_0855
1

detected by
an unknotting move
-3+10t-18t^2+23t^3-18t^4+10t^5-3t^6
Seifert matrix of 12n_0855
1 -1 0 0 -1 0
-1 0 0 -1 -1 0
0 -1 -1 0 -1 -1
1 -1 0 1 -1 0
0 -2 0 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,-1+3t+4t^2+5t^3+5t^4,-t^2-t^3-2t^4,1-t^3-t^4,1+t+t^2,0)
the Blanchfield form on it
-14t^-5+33t^-4-44t^-3+59t^-2-74t^-1+88-74t+59t^2-44t^3+33t^4-14t^5
85
First homology
of the double branched cover of 12n_0855
Z/85
0 0
12n_0856
2

detected by
the Lickorish test
-5+14t-17t^2+14t^3-5t^4
Seifert matrix of 12n_0856
1 -1 0 -1
-1 -1 -1 -2
1 -1 1 -1
0 -3 0 -2
1 or 2
55
First homology
of the double branched cover of 12n_0856
Z/55
2 2
12n_0857
1

detected by
an unknotting move
-1+6t-17t^2+29t^3-33t^4+29t^5-17t^6+6t^7-t^8
Seifert matrix of 12n_0857
1 0 0 0 1 1 0 1
-1 -1 0 0 -1 -1 0 0
0 0 -1 0 0 0 -1 0
0 0 0 1 0 0 0 0
0 0 0 -1 1 1 -1 1
0 0 -1 -1 0 1 -1 1
0 0 0 0 0 0 -1 0
0 0 -1 -1 0 0 -1 1
1
Generator of the Alexander module
(0,2-t,0,0,1-t,1-t,0,0)
the Blanchfield form on it
t^-3-5t^-2+12t^-1-16+12t-5t^2+t^3
139
First homology
of the double branched cover of 12n_0857
Z/139
2 2
12n_0858
1

detected by
an unknotting move
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 12n_0858
0 0 1 1 -1 1
0 -1 -1 -1 0 -1
1 0 2 1 -1 1
1 0 1 2 0 1
0 0 0 0 1 0
1 0 2 1 -1 2
1
Generator of the Alexander module
(t,-2t,0,1,0,1+t)
the Blanchfield form on it
t^-1-2+t
111
First homology
of the double branched cover of 12n_0858
Z/111
2 2
12n_0859
1

detected by
an unknotting move
1-6t+16t^2-31t^3+41t^4-31t^5+16t^6-6t^7+t^8
Seifert matrix of 12n_0859
1 0 0 0 1 0 0 1
-1 -1 0 0 -1 0 0 0
0 0 -1 0 0 0 -1 0
0 0 0 1 0 0 0 0
0 0 -1 -1 1 0 -1 1
0 0 -1 0 0 -1 -1 0
0 0 0 0 0 0 -1 0
0 0 -1 -1 0 -1 -1 1
1 or 2
149
First homology
of the double branched cover of 12n_0859
Z/149
0 0
12n_0860
2

detected by
the Lickorish test
3-15t+33t^2-41t^3+33t^4-15t^5+3t^6
Seifert matrix of 12n_0860
3 4 4 2 2 2
2 5 4 2 2 2
2 5 5 2 2 2
3 4 4 3 2 2
2 3 3 2 1 1
3 4 4 3 2 1
1 or 2
143
First homology
of the double branched cover of 12n_0860
Z/143
2 2
12n_0861
1

detected by
an unknotting move
2-9t+22t^2-29t^3+22t^4-9t^5+2t^6
Seifert matrix of 12n_0861
-1 0 0 0 0 0
0 0 0 1 0 -1
0 0 -2 -1 -1 0
1 1 0 -2 -1 1
1 0 -1 -1 -2 0
-1 0 0 1 1 0
1
Generator of the Alexander module
(0,1,0,0,1,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
95
First homology
of the double branched cover of 12n_0861
Z/95
-2 2
12n_0862
1

detected by
an unknotting move
3-13t+29t^2-37t^3+29t^4-13t^5+3t^6
Seifert matrix of 12n_0862
1 0 0 0 0 0
0 -1 1 0 1 1
0 0 -2 0 -1 -1
1 -1 1 0 1 0
0 0 -1 0 -2 -1
-1 1 -1 -1 -2 -1
1
Generator of the Alexander module
(2t+2t^2,-2-t,1,1+t,1,-t)
the Blanchfield form on it
17t^-3-87t^-2+209t^-1-270+209t-87t^2+17t^3
127
First homology
of the double branched cover of 12n_0862
Z/127
-2 2
12n_0863
2

detected by
the signature
-3+16t-33t^2+41t^3-33t^4+16t^5-3t^6
Seifert matrix of 12n_0863
-6 -9 0 0 -9 3
-5 -5 0 -1 -6 2
2 3 -1 0 3 -1
-1 -3 0 0 -3 1
-9 -11 0 -1 -14 3
0 1 0 0 0 -1
1 or 2
145
First homology
of the double branched cover of 12n_0863
Z/145
-4 4
12n_0864 1 or 2
1-5t+15t^2-28t^3+33t^4-28t^5+15t^6-5t^7+t^8
Seifert matrix of 12n_0864
-1 0 0 0 0 0 0 0
1 1 0 1 1 1 1 1
-1 0 -1 0 -1 -1 0 -1
0 0 0 1 0 1 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 -1 -1 0 -1
1 0 0 1 1 1 1 1
0 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,-t-t^2+t^3,1+2t+t^2-t^3,1+t-t^2,-1,t,1-t^2,t)
the Blanchfield form on it
t^-3-4t^-2+10t^-1-15+10t-4t^2+t^3
131
First homology
of the double branched cover of 12n_0864
Z/131
-2 2
12n_0865
1

detected by
an unknotting move
1-4t+11t^2-21t^3+25t^4-21t^5+11t^6-4t^7+t^8
Seifert matrix of 12n_0865
-1 0 0 0 0 0 0 0
1 1 0 1 1 1 1 1
-1 0 -1 0 0 -1 0 0
0 0 0 1 0 0 0 0
0 0 0 1 1 1 0 1
0 0 0 0 0 -1 0 0
1 0 0 1 1 1 1 1
0 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,-2t-4t^2+t^3+5t^4-3t^5,1-2t^2+8t^3-3t^4,2+3t-4t^2-5t^3+3t^4,1+3t+3t^2+3t^3+2t^4-3t^5,1+3t,-2t-3t^2+3t^3+2t^4-3t^5,1+t-3t^2+4t^3+5t^4-3t^5)
the Blanchfield form on it
x
99
First homology
of the double branched cover of 12n_0865
Z/99
2 2
12n_0866
1

detected by
an unknotting move
-1+5t-15t^2+30t^3-39t^4+30t^5-15t^6+5t^7-t^8
Seifert matrix of 12n_0866
-1 0 0 0 0 0 0 0
1 1 0 1 1 1 1 1
-1 0 -1 0 -1 -1 0 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 -1 -1 0 0
1 0 0 1 1 1 1 1
0 0 0 1 0 1 0 1
1 or 2
141
First homology
of the double branched cover of 12n_0866
Z/141
0 0
12n_0867
2

detected by
the signature
-2+14t-31t^2+39t^3-31t^4+14t^5-2t^6
Seifert matrix of 12n_0867
0 0 0 0 -1 0
0 1 0 0 0 0
0 0 2 0 1 0
-1 0 0 0 -1 0
-1 1 0 -1 0 0
-1 0 -1 -1 -1 1
1
Generator of the Alexander module
(0,0,1,1,t,2t)
the Blanchfield form on it
-2t^-2+4t^-1-5+4t-2t^2
133
First homology
of the double branched cover of 12n_0867
Z/133
4 4
12n_0868
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 12n_0868
-2 0 2 0
-1 0 0 0
0 -1 -2 0
-2 0 1 1
1
Generator of the Alexander module
(0,0,2,1)
the Blanchfield form on it
-1
33
First homology
of the double branched cover of 12n_0868
Z/33
0 0
12n_0869
2

detected by
the Nakanishi index
2-12t+32t^2-43t^3+32t^4-12t^5+2t^6
Seifert matrix of 12n_0869
-1 0 -1 0 0 0
0 0 -1 0 0 -1
0 -1 -2 0 0 -1
1 1 1 1 -1 0
0 1 1 0 -1 1
0 -1 -1 0 0 -2
2
135
First homology
of the double branched cover of 12n_0869
Z/45+Z/3
-2 2
12n_0870
2

detected by
the Lickorish test
-1+3t-5t^2+7t^3-5t^4+3t^5-t^6
Seifert matrix of 12n_0870
1 0 0 0 0 0
-1 -1 -1 0 -1 0
0 1 -1 0 0 0
-2 2 -2 2 -1 1
-1 0 -1 0 0 0
-1 1 -1 1 0 0
1
Generator of the Alexander module
(0,-t,-t^2+t^3-2t^4+t^5,1+3t-2t^2-5t^4+2t^5,-t,t-2t^4+t^5)
the Blanchfield form on it
-t^-1+1-t
25
First homology
of the double branched cover of 12n_0870
Z/25
0 0
12n_0871
1

detected by
an unknotting move
1-9t+29t^2-41t^3+29t^4-9t^5+t^6
Seifert matrix of 12n_0871
-1 0 0 0 0 0
-1 -1 -1 0 -1 0
0 1 -1 0 0 0
-2 2 -2 2 -1 1
-1 0 -1 0 0 0
-1 1 -1 1 0 0
1
Generator of the Alexander module
(-4t^2+8t^3+68t^4-324t^5+524t^6+188t^7-1900t^8+2976t^9-2392t^10+1088t^11-256t^12+24t^13,2+10t-26t^2-24t^3+346t^4-756t^5+772t^6-428t^7+116t^8-12t^9,1-2t-6t^2+88t^3-348t^4+686t^5-464t^6-1134t^7+3388t^8-4172t^9+2936t^10-1216t^11+268t^12-24t^13,2-30t^2+116t^3-142t^4-284t^5+1516t^6-3322t^7+4240t^8-3288t^
the Blanchfield form on it
x
119
First homology
of the double branched cover of 12n_0871
Z/119
-2 2
12n_0872
1

detected by
an unknotting move
-1+6t-16t^2+27t^3-31t^4+27t^5-16t^6+6t^7-t^8
Seifert matrix of 12n_0872
1 0 -1 0 1 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
1 -1 -1 1 1 1 -1 0
0 0 0 0 1 0 0 0
1 0 -1 0 1 1 -1 0
0 0 0 0 0 0 1 0
-1 0 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,2t-2t^2+4t^3-4t^4+2t^5-2t^6,-1-2t^2-t^4,0,-t-2t^3-t^5,-2t-2t^2-2t^3-4t^4+2t^5-2t^6+2t^7,0,-2-4t+t^2-6t^3+7t^4-3t^5+3t^6-t^8)
the Blanchfield form on it
x
131
First homology
of the double branched cover of 12n_0872
Z/131
2 2
12n_0873
2

detected by
A(F_2)
1-5t+10t^2-16t^3+21t^4-16t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0873
1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
-1 -1 -1 -1 -1 -1 -1 0
0 -1 0 -1 0 0 0 0
0 0 0 0 -1 0 0 0
1 0 0 0 0 1 0 0
-1 -1 0 -1 -1 -1 -1 0
1 0 0 0 1 1 0 1
2
85
First homology
of the double branched cover of 12n_0873
Z/85
0 0
12n_0874
2

detected by
the Lickorish test
-1+5t-14t^2+26t^3-31t^4+26t^5-14t^6+5t^7-t^8
Seifert matrix of 12n_0874
1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
-1 -1 -1 -1 -1 -1 -1 0
0 -1 0 -1 0 0 0 0
0 0 0 0 -1 0 0 0
1 0 0 0 0 1 0 0
-1 -1 0 -1 -1 -1 -1 0
1 0 0 0 1 1 0 -1
2
123
First homology
of the double branched cover of 12n_0874
Z/123
-2 2
12n_0875
1

detected by
an unknotting move
-1+4t-11t^2+21t^3-25t^4+21t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0875
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
0 -1 -1 0 0 -1 0 0
0 0 0 -1 0 0 0 -1
1 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 -1 0 0 -1 -1
1 0 0 0 1 -1 0 -1
1 or 2
99
First homology
of the double branched cover of 12n_0875
Z/99
-2 2
12n_0876
2

detected by
the Nakanishi index
-2+8t-18t^2+25t^3-18t^4+8t^5-2t^6
Seifert matrix of 12n_0876
1 0 0 0 0 0
1 1 0 0 1 0
0 -1 -1 0 0 -1
-1 0 0 -2 -1 1
1 0 0 0 1 0
0 0 0 0 0 -1
2
81
First homology
of the double branched cover of 12n_0876
Z/9+Z/9
0 0
12n_0877
2

detected by
the Lickorish test
-1+7t-20t^2+32t^3-35t^4+32t^5-20t^6+7t^7-t^8
Seifert matrix of 12n_0877
-1 -1 0 0 0 0 -1 -1
0 1 0 0 0 -1 0 1
-1 0 1 -1 0 0 0 0
-1 0 0 -1 0 0 -1 -1
0 1 0 0 1 -1 0 1
0 0 0 0 0 1 0 0
0 -1 0 0 -1 0 -1 -1
0 0 0 0 0 0 0 1
2
155
First homology
of the double branched cover of 12n_0877
Z/155
2 2
12n_0878
2

detected by
A(F_2)
1-11t+34t^2-47t^3+34t^4-11t^5+t^6
Seifert matrix of 12n_0878
1 0 0 0 0 0
-1 -1 -1 -1 0 -2
0 0 -2 1 0 0
0 -1 0 -2 0 -1
-1 -1 0 -1 -1 -1
-1 -1 -1 -1 0 -1
2
139
First homology
of the double branched cover of 12n_0878
Z/139
-2 2
12n_0879
2

detected by
the Lickorish test
-1+6t-17t^2+30t^3-35t^4+30t^5-17t^6+6t^7-t^8
Seifert matrix of 12n_0879
1 0 -1 0 0 0 0 -1
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 0
1 0 -1 1 0 -1 0 -1
0 -1 -1 0 1 -1 0 -1
0 -1 0 0 0 -1 0 0
1 -1 -1 1 0 -1 1 -1
0 0 0 0 0 0 0 1
2
143
First homology
of the double branched cover of 12n_0879
Z/143
2 2
12n_0880
1

detected by
an unknotting move
-3+14t-30t^2+39t^3-30t^4+14t^5-3t^6
Seifert matrix of 12n_0880
1 2 0 1 2 2
3 3 0 2 4 3
2 2 1 1 2 1
3 3 0 1 2 3
4 4 0 1 3 4
1 2 0 1 2 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
3t^-2-11t^-1+15-11t+3t^2
133
First homology
of the double branched cover of 12n_0880
Z/133
0 0
12n_0881
2

detected by
the Nakanishi index
9-30t+43t^2-30t^3+9t^4
Seifert matrix of 12n_0881
-2 0 -1 0
-1 -2 0 -1
-1 0 -2 0
-1 -1 -1 -2
2
121
First homology
of the double branched cover of 12n_0881
Z/11+Z/11
-4 4
12n_0882
3

detected by
the signature
1-6t+13t^2-19t^3+21t^4-19t^5+13t^6-6t^7+t^8
Seifert matrix of 12n_0882
0 0 0 0 1 0 0 0
-1 1 1 0 0 0 1 -1
0 0 1 0 0 0 1 0
0 0 0 1 1 0 0 0
1 0 -1 0 0 0 -1 1
-1 1 1 0 0 1 1 -1
0 0 0 0 0 0 1 0
-1 0 0 0 1 0 0 0
1 or 2
99
First homology
of the double branched cover of 12n_0882
Z/99
6 6
12n_0883
2

detected by
the Nakanishi index
3-12t+22t^2-25t^3+22t^4-12t^5+3t^6
Seifert matrix of 12n_0883
-1 -1 -1 -1 0 -1
0 -1 0 -1 0 -1
0 0 1 0 0 0
0 0 0 -1 0 -1
0 0 1 0 1 2
0 0 1 0 2 1
2
99
First homology
of the double branched cover of 12n_0883
Z/33+Z/3
-2 2
12n_0884
1

detected by
an unknotting move
5-20t+31t^2-20t^3+5t^4
Seifert matrix of 12n_0884
-5 -3 0 -2
-4 -1 1 -2
-2 -1 1 -1
-3 -2 0 -2
1
Generator of the Alexander module
(0,1,1,0)
the Blanchfield form on it
-1
81
First homology
of the double branched cover of 12n_0884
Z/81
0 0
12n_0885
1

detected by
an unknotting move
-2+13t-35t^2+49t^3-35t^4+13t^5-2t^6
Seifert matrix of 12n_0885
-1 -1 -1 1 -1 0
0 1 1 0 0 0
0 0 1 0 0 0
0 1 0 1 1 0
0 0 0 0 -2 1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(-t,0,0,-2,1,0)
the Blanchfield form on it
-2t^-2+9t^-1-15+9t-2t^2
149
First homology
of the double branched cover of 12n_0885
Z/149
0 0
12n_0886
2

detected by
the Lickorish test
2-13t+38t^2-53t^3+38t^4-13t^5+2t^6
Seifert matrix of 12n_0886
1 0 -1 0 0 0
0 -1 0 -1 0 0
0 0 -1 1 0 0
0 0 0 -2 0 0
1 1 -1 1 1 0
-1 0 1 -1 -1 -1
1 or 2
159
First homology
of the double branched cover of 12n_0886
Z/159
-2 2
12n_0887
2

detected by
the Nakanishi index
-1+6t-16t^2+25t^3-29t^4+25t^5-16t^6+6t^7-t^8
Seifert matrix of 12n_0887
2 0 1 0 2 1 2 0
-1 -1 -1 0 0 -1 -1 0
2 0 0 0 1 1 2 0
1 -1 0 -1 0 0 1 -1
0 0 0 0 1 0 0 0
1 0 0 0 1 0 1 0
3 0 1 0 2 1 2 0
-1 -1 -1 0 -1 -1 -1 -1
2
125
First homology
of the double branched cover of 12n_0887
Z/25+Z/5
-4 4
12n_0888
4

detected by
the signature
-1+t+t^2-6t^3+11t^4-13t^5+11t^6-6t^7+t^8+t^9-t^10
Seifert matrix of 12n_0888
-1 0 0 0 0 -1 -1 0 0 -1
0 -1 -1 -1 0 0 0 -1 -1 0
0 0 -1 -1 0 0 0 -1 0 0
0 0 0 -1 0 0 0 0 0 0
-1 0 0 0 -1 -1 -1 0 0 -1
0 0 -1 -1 0 -1 -1 -1 0 -1
0 0 -1 -1 0 0 -1 -1 0 0
0 0 0 -1 0 0 0 -1 0 0
0 0 -1 -1 0 0 0 -1 -1 0
0 0 -1 -1 0 0 -1 -1 0 -1
2
45
First homology
of the double branched cover of 12n_0888
Z/15+Z/3
-8 8
12n_0888
4

detected by
the signature
-1+t+t^2-6t^3+11t^4-13t^5+11t^6-6t^7+t^8+t^9-t^10
Seifert matrix of 12n_0888
-1 0 0 0 0 -1 -1 0 0 -1
0 -1 -1 -1 0 0 0 -1 -1 0
0 0 -1 -1 0 0 0 -1 0 0
0 0 0 -1 0 0 0 0 0 0
-1 0 0 0 -1 -1 -1 0 0 -1
0 0 -1 -1 0 -1 -1 -1 0 -1
0 0 -1 -1 0 0 -1 -1 0 0
0 0 0 -1 0 0 0 -1 0 0
0 0 -1 -1 0 0 0 -1 -1 0
0 0 -1 -1 0 0 -1 -1 0 -1
2
45
First homology
of the double branched cover of 12n_0888
Z/15+Z/3
-8 8