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 |

Knot | u_a | Alexander polynomial | Nak. index | det. | sign | max LT. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_1 | 1 detected by an unknotting move | -4+9t-4t^2 Seifert matrix of 10_1
| 1 Generator of the Alexander module (0,1) the Blanchfield form on it t^-1-2+t | 17 First homology of the double branched cover of 10_1 Z/17 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_2 | 3 detected by the signature | -1+3t-3t^2+3t^3-3t^4+3t^5-3t^6+3t^7-t^8 Seifert matrix of 10_2
| 1 Generator of the Alexander module (0,0,0,0,1,0,0,0) the Blanchfield form on it -t^-3+3t^-2-3t^-1+3-3t+3t^2-t^3 | 23 First homology of the double branched cover of 10_2 Z/23 | -6 | 6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_3 | 2 detected by the Lickorish test | -6+13t-6t^2 Seifert matrix of 10_3
| 1 Generator of the Alexander module (1,0) the Blanchfield form on it 2t^-1-4+2t | 25 First homology of the double branched cover of 10_3 Z/25 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_4 | 1 detected by an unknotting move | -3+7t-7t^2+7t^3-3t^4 Seifert matrix of 10_4
| 1 Generator of the Alexander module (0,0,1,0) the Blanchfield form on it t^-2-2t^-1+2-2t+t^2 | 27 First homology of the double branched cover of 10_4 Z/27 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_5 | 2 detected by the signature | 1-3t+5t^2-5t^3+5t^4-5t^5+5t^6-3t^7+t^8 Seifert matrix of 10_5
| 1 Generator of the Alexander module (0,0,0,2,2,0,0,-1) the Blanchfield form on it t^-3-t^-2+t^-1-1+t-t^2+t^3 | 33 First homology of the double branched cover of 10_5 Z/33 | 4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_6 | 2 detected by the signature | -2+6t-7t^2+7t^3-7t^4+6t^5-2t^6 Seifert matrix of 10_6
| 1 Generator of the Alexander module (-2,0,0,1,0,0) the Blanchfield form on it -5t^-3+11t^-2-12t^-1+12-12t+11t^2-5t^3 | 37 First homology of the double branched cover of 10_6 Z/37 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_7 | 1 detected by an unknotting move | -3+11t-15t^2+11t^3-3t^4 Seifert matrix of 10_7
| 1 Generator of the Alexander module (0,0,0,1) the Blanchfield form on it t^-2-4t^-1+6-4t+t^2 | 43 First homology of the double branched cover of 10_7 Z/43 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_8 | 2 detected by the signature | -2+5t-5t^2+5t^3-5t^4+5t^5-2t^6 Seifert matrix of 10_8
| 1 Generator of the Alexander module (0,0,0,1,0,0) 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 10_8 Z/29 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_9 | 1 detected by an unknotting move | -1+3t-5t^2+7t^3-7t^4+7t^5-5t^6+3t^7-t^8 Seifert matrix of 10_9
| 1 Generator of the Alexander module (0,0,2,1,1,t,1,1) the Blanchfield form on it 1 | 39 First homology of the double branched cover of 10_9 Z/39 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_10 | 1 detected by an unknotting move | 3-11t+17t^2-11t^3+3t^4 Seifert matrix of 10_10
| 1 Generator of the Alexander module (0,1,1,0) the Blanchfield form on it 1 | 45 First homology of the double branched cover of 10_10 Z/45 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_11 | 1 detected by an unknotting move | -4+11t-13t^2+11t^3-4t^4 Seifert matrix of 10_11
| 1 or 2 | 43 First homology of the double branched cover of 10_11 Z/43 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_12 | 1 detected by an unknotting move | 2-6t+10t^2-11t^3+10t^4-6t^5+2t^6 Seifert matrix of 10_12
| 1 Generator of the Alexander module (0,0,0,0,0,1) the Blanchfield form on it t^-3-3t^-2+5t^-1-6+5t-3t^2+t^3 | 47 First homology of the double branched cover of 10_12 Z/47 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_13 | 1 detected by an unknotting move | 2-13t+23t^2-13t^3+2t^4 Seifert matrix of 10_13
| 1 Generator of the Alexander module (0,-2-27t+99t^2-144t^3+84t^4-16t^5,0,3+35t-167t^2+304t^3-266t^4+108t^5-16t^6) the Blanchfield form on it 357953t^-2-2326696t^-1+4116466-2326696t+357953t^2 | 53 First homology of the double branched cover of 10_13 Z/53 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_14 | 2 detected by the signature | -2+8t-12t^2+13t^3-12t^4+8t^5-2t^6 Seifert matrix of 10_14
| 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 | 57 First homology of the double branched cover of 10_14 Z/57 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_15 | 1 detected by an unknotting move | 2-6t+9t^2-9t^3+9t^4-6t^5+2t^6 Seifert matrix of 10_15
| 1 Generator of the Alexander module (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 10_15 Z/43 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_16 | 1 detected by an unknotting move | -4+12t-15t^2+12t^3-4t^4 Seifert matrix of 10_16
| 1 or 2 | 47 First homology of the double branched cover of 10_16 Z/47 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_17 | 1 detected by an unknotting move | 1-3t+5t^2-7t^3+9t^4-7t^5+5t^6-3t^7+t^8 Seifert matrix of 10_17
| 1 Generator of the Alexander module (0,0,0,0,0,1,0,0) the Blanchfield form on it -1 | 41 First homology of the double branched cover of 10_17 Z/41 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_18 | 1 detected by an unknotting move | -4+14t-19t^2+14t^3-4t^4 Seifert matrix of 10_18
| 1 or 2 | 55 First homology of the double branched cover of 10_18 Z/55 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_19 | 2 detected by the Lickorish test | 2-7t+11t^2-11t^3+11t^4-7t^5+2t^6 Seifert matrix of 10_19
| 1 or 2 | 51 First homology of the double branched cover of 10_19 Z/51 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_20 | 2 detected by the Lickorish test | -3+9t-11t^2+9t^3-3t^4 Seifert matrix of 10_20
| 1 Generator of the Alexander module (0,0,1,0) the Blanchfield form on it t^-2-3t^-1+4-3t+t^2 | 35 First homology of the double branched cover of 10_20 Z/35 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_21 | 2 detected by the signature | -2+7t-9t^2+9t^3-9t^4+7t^5-2t^6 Seifert matrix of 10_21
| 1 Generator of the Alexander module (0,0,0,1,0,0) the Blanchfield form on it t^-3-4t^-2+6t^-1-6+6t-4t^2+t^3 | 45 First homology of the double branched cover of 10_21 Z/45 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_22 | 1 detected by an unknotting move | -2+6t-10t^2+13t^3-10t^4+6t^5-2t^6 Seifert matrix of 10_22
| 1 Generator of the Alexander module (0,0,0,0,1,0) the Blanchfield form on it t^-3-3t^-2+5t^-1-6+5t-3t^2+t^3 | 49 First homology of the double branched cover of 10_22 Z/49 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_23 | 1 detected by an unknotting move | 2-7t+13t^2-15t^3+13t^4-7t^5+2t^6 Seifert matrix of 10_23
| 1 Generator of the Alexander module (0,0,0,t,1+t,0) the Blanchfield form on it 2t^-2-3t^-1+3-3t+2t^2 | 59 First homology of the double branched cover of 10_23 Z/59 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_24 | 2 detected by the Lickorish test | -4+14t-19t^2+14t^3-4t^4 Seifert matrix of 10_24
| 1 or 2 | 55 First homology of the double branched cover of 10_24 Z/55 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_25 | 2 detected by the signature | -2+8t-14t^2+17t^3-14t^4+8t^5-2t^6 Seifert matrix of 10_25
| 1 Generator of the Alexander module (0,0,0,1,0,0) the Blanchfield form on it -2t^-2+7t^-1-9+7t-2t^2 | 65 First homology of the double branched cover of 10_25 Z/65 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_26 | 1 detected by an unknotting move | -2+7t-13t^2+17t^3-13t^4+7t^5-2t^6 Seifert matrix of 10_26
| 1 Generator of the Alexander module (0,0,0,1,0,0) the Blanchfield form on it t^-3-4t^-2+8t^-1-10+8t-4t^2+t^3 | 61 First homology of the double branched cover of 10_26 Z/61 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_27 | 1 detected by an unknotting move | 2-8t+16t^2-19t^3+16t^4-8t^5+2t^6 Seifert matrix of 10_27
| 1 Generator of the Alexander module (0,0,0,t,1+t,0) the Blanchfield form on it 2t^-2-4t^-1+5-4t+2t^2 | 71 First homology of the double branched cover of 10_27 Z/71 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_28 | 1 detected by an unknotting move | 4-13t+19t^2-13t^3+4t^4 Seifert matrix of 10_28
| 1 Generator of the Alexander module (0,0,-1,1) the Blanchfield form on it 2t^-1-3+2t | 53 First homology of the double branched cover of 10_28 Z/53 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_29 | 2 detected by the Lickorish test | 1-7t+15t^2-17t^3+15t^4-7t^5+t^6 Seifert matrix of 10_29
| 1 Generator of the Alexander module (0,0,0,1+t,0,t^2) the Blanchfield form on it t^-2-7t^-1+13-7t+t^2 | 63 First homology of the double branched cover of 10_29 Z/63 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_30 | 1 detected by an unknotting move | -4+17t-25t^2+17t^3-4t^4 Seifert matrix of 10_30
| 1 Generator of the Alexander module (0,1,0,0) the Blanchfield form on it 1 | 67 First homology of the double branched cover of 10_30 Z/67 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_31 | 1 detected by an unknotting move | 4-14t+21t^2-14t^3+4t^4 Seifert matrix of 10_31
| 1 or 2 | 57 First homology of the double branched cover of 10_31 Z/57 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_32 | 1 detected by an unknotting move | -2+8t-15t^2+19t^3-15t^4+8t^5-2t^6 Seifert matrix of 10_32
| 1 Generator of the Alexander module (-t,0,0,1,0,0) the Blanchfield form on it -t^-2+3t^-1-3+3t-t^2 | 69 First homology of the double branched cover of 10_32 Z/69 | 0 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_33 | 1 detected by an unknotting move | 4-16t+25t^2-16t^3+4t^4 Seifert matrix of 10_33
| 1 or 2 | 65 First homology of the double branched cover of 10_33 Z/65 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_34 | 1 detected by an unknotting move | 3-9t+13t^2-9t^3+3t^4 Seifert matrix of 10_34
| 1 Generator of the Alexander module (0,0,1,0) the Blanchfield form on it t^-2-3t^-1+4-3t+t^2 | 37 First homology of the double branched cover of 10_34 Z/37 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_35 | 1 detected by an unknotting move | 2-12t+21t^2-12t^3+2t^4 Seifert matrix of 10_35
| 1 Generator of the Alexander module (0,0,1,-1) the Blanchfield form on it -t^-1+3-t | 49 First homology of the double branched cover of 10_35 Z/49 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_36 | 2 detected by the Lickorish test | -3+13t-19t^2+13t^3-3t^4 Seifert matrix of 10_36
| 1 Generator of the Alexander module (0,0,1,0) the Blanchfield form on it -t^-1+3-t | 51 First homology of the double branched cover of 10_36 Z/51 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_37 | 1 detected by an unknotting move | 4-13t+19t^2-13t^3+4t^4 Seifert matrix of 10_37
| 1 Generator of the Alexander module (-2t+t^2,0,-2+t,1-4t+2t^2) the Blanchfield form on it -4t^-1+7-4t | 53 First homology of the double branched cover of 10_37 Z/53 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_38 | 1 detected by an unknotting move | -4+15t-21t^2+15t^3-4t^4 Seifert matrix of 10_38
| 1 Generator of the Alexander module (0,0,0,1) the Blanchfield form on it 2t^-2-7t^-1+10-7t+2t^2 | 59 First homology of the double branched cover of 10_38 Z/59 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_39 | 2 detected by the signature | -2+8t-13t^2+15t^3-13t^4+8t^5-2t^6 Seifert matrix of 10_39
| 1 Generator of the Alexander module (0,0,0,1,0,0) the Blanchfield form on it -t^-2+3t^-1-3+3t-t^2 | 61 First homology of the double branched cover of 10_39 Z/61 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_40 | 2 detected by the Lickorish test | 2-8t+17t^2-21t^3+17t^4-8t^5+2t^6 Seifert matrix of 10_40
| 1 Generator of the Alexander module (0,0,0,0,1,1) the Blanchfield form on it -t^-2+3t^-1-5+3t-t^2 | 75 First homology of the double branched cover of 10_40 Z/75 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_41 | 1 detected by an unknotting move | 1-7t+17t^2-21t^3+17t^4-7t^5+t^6 Seifert matrix of 10_41
| 1 Generator of the Alexander module (0,1,1+3t-4t^2+t^3,2-2t,1-2t+3t^2-t^3,0) the Blanchfield form on it t^-2-7t^-1+14-7t+t^2 | 71 First homology of the double branched cover of 10_41 Z/71 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_42 | 1 detected by an unknotting move | -1+7t-19t^2+27t^3-19t^4+7t^5-t^6 Seifert matrix of 10_42
| 1 Generator of the Alexander module (0,0,0,0,0,1) the Blanchfield form on it 2t^-2-7t^-1+11-7t+2t^2 | 81 First homology of the double branched cover of 10_42 Z/81 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_43 | 1 detected by an unknotting move | -1+7t-17t^2+23t^3-17t^4+7t^5-t^6 Seifert matrix of 10_43
| 1 Generator of the Alexander module (0,0,0,0,1,0) the Blanchfield form on it -t^-1+1-t | 73 First homology of the double branched cover of 10_43 Z/73 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_44 | 1 detected by an unknotting move | 1-7t+19t^2-25t^3+19t^4-7t^5+t^6 Seifert matrix of 10_44
| 1 Generator of the Alexander module (0,0,-1,1,0,-1) the Blanchfield form on it t^-2-5t^-1+8-5t+t^2 | 79 First homology of the double branched cover of 10_44 Z/79 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_45 | 1 detected by an unknotting move | -1+7t-21t^2+31t^3-21t^4+7t^5-t^6 Seifert matrix of 10_45
| 1 Generator of the Alexander module (t^2,-t-2t^2-2t^3+3t^4+4t^5+t^6,1-3t^2-t^3,-1+3t^2+4t^3+t^4,1+t-3t^2-t^3,2+t-6t^2-2t^3) the Blanchfield form on it x | 89 First homology of the double branched cover of 10_45 Z/89 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_46 | 3 detected by the signature | -1+3t-4t^2+5t^3-5t^4+5t^5-4t^6+3t^7-t^8 Seifert matrix of 10_46
| 1 Generator of the Alexander module (0,1,-t,0,0,0,0,0) the Blanchfield form on it -t^-3+2t^-2-2t^-1+2-2t+2t^2-t^3 | 31 First homology of the double branched cover of 10_46 Z/31 | -6 | 6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_47 | 2 detected by the signature | -1+3t-6t^2+7t^3-7t^4+7t^5-6t^6+3t^7-t^8 Seifert matrix of 10_47
| 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 | 41 First homology of the double branched cover of 10_47 Z/41 | 4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_48 | 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 10_48
| 1 Generator of the Alexander module (0,0,-t,0,1,0,0,0) 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 10_48 Z/49 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_49 | 3 detected by the signature | 3-8t+12t^2-13t^3+12t^4-8t^5+3t^6 Seifert matrix of 10_49
| 1 Generator of the Alexander module (t,0,0,1,0,0) the Blanchfield form on it 3t^-2-4t^-1+4-4t+3t^2 | 59 First homology of the double branched cover of 10_49 Z/59 | -6 | 6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_50 | 2 detected by the signature | -2+7t-11t^2+13t^3-11t^4+7t^5-2t^6 Seifert matrix of 10_50
| 1 Generator of the Alexander module (0,0,-1,0,1,1) the Blanchfield form on it -6t^-2+17t^-1-19+17t-6t^2 | 53 First homology of the double branched cover of 10_50 Z/53 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_51 | 1 detected by an unknotting move | 2-7t+15t^2-19t^3+15t^4-7t^5+2t^6 Seifert matrix of 10_51
| 1 Generator of the Alexander module (0,0,0,-2t,1,0) the Blanchfield form on it 5t^-3-18t^-2+39t^-1-50+39t-18t^2+5t^3 | 67 First homology of the double branched cover of 10_51 Z/67 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_52 | 1 detected by an unknotting move | 2-7t+13t^2-15t^3+13t^4-7t^5+2t^6 Seifert matrix of 10_52
| 1 Generator of the Alexander module (0,0,t-t^4,0,0,1+t-t^3) the Blanchfield form on it 2t^-2-5t^-1+8-5t+2t^2 | 59 First homology of the double branched cover of 10_52 Z/59 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_53 | 2 detected by the signature | 6-18t+25t^2-18t^3+6t^4 Seifert matrix of 10_53
| 1 Generator of the Alexander module (0,0,1,-2) the Blanchfield form on it -17t^-2+56t^-1-78+56t-17t^2 | 73 First homology of the double branched cover of 10_53 Z/73 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_54 | 1 detected by an unknotting move | 2-6t+10t^2-11t^3+10t^4-6t^5+2t^6 Seifert matrix of 10_54
| 1 Generator of the Alexander module (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 10_54 Z/47 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_55 | 2 detected by the signature | 5-15t+21t^2-15t^3+5t^4 Seifert matrix of 10_55
| 1 Generator of the Alexander module (1,0,0,0) the Blanchfield form on it 3t^-1-5+3t | 61 First homology of the double branched cover of 10_55 Z/61 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_56 | 2 detected by the signature | -2+8t-14t^2+17t^3-14t^4+8t^5-2t^6 Seifert matrix of 10_56
| 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 | 65 First homology of the double branched cover of 10_56 Z/65 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_57 | 1 detected by an unknotting move | 2-8t+18t^2-23t^3+18t^4-8t^5+2t^6 Seifert matrix of 10_57
| 1 Generator of the Alexander module (0,0,0,0,0,1) the Blanchfield form on it t^-3-5t^-2+12t^-1-16+12t-5t^2+t^3 | 79 First homology of the double branched cover of 10_57 Z/79 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_58 | 1 detected by an unknotting move | 3-16t+27t^2-16t^3+3t^4 Seifert matrix of 10_58
| 1 Generator of the Alexander module (0,0,t,1) the Blanchfield form on it 2t^-1-5+2t | 65 First homology of the double branched cover of 10_58 Z/65 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_59 | 1 detected by an unknotting move | 1-7t+18t^2-23t^3+18t^4-7t^5+t^6 Seifert matrix of 10_59
| 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 | 75 First homology of the double branched cover of 10_59 Z/75 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_60 | 1 detected by an unknotting move | -1+7t-20t^2+29t^3-20t^4+7t^5-t^6 Seifert matrix of 10_60
| 1 Generator of the Alexander module (0,0,0,0,0,1) the Blanchfield form on it 1 | 85 First homology of the double branched cover of 10_60 Z/85 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_61 | 2 detected by the signature | -2+5t-6t^2+7t^3-6t^4+5t^5-2t^6 Seifert matrix of 10_61
| 2 | 33 First homology of the double branched cover of 10_61 Z/33 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_62 | 2 detected by the signature | 1-3t+6t^2-8t^3+9t^4-8t^5+6t^6-3t^7+t^8 Seifert matrix of 10_62
| 1 Generator of the Alexander module (0,0,0,1,0,0,0,0) the Blanchfield form on it -t^-3+3t^-2-5t^-1+5-5t+3t^2-t^3 | 45 First homology of the double branched cover of 10_62 Z/45 | 4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_63 | 2 detected by the signature | 5-14t+19t^2-14t^3+5t^4 Seifert matrix of 10_63
| 2 | 57 First homology of the double branched cover of 10_63 Z/57 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_64 | 1 detected by an unknotting move | -1+3t-6t^2+10t^3-11t^4+10t^5-6t^6+3t^7-t^8 Seifert matrix of 10_64
| 1 Generator of the Alexander module (0,0,0,0,0,1,0,0) the Blanchfield form on it -t^-3+3t^-2-5t^-1+7-5t+3t^2-t^3 | 51 First homology of the double branched cover of 10_64 Z/51 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_65 | 2 detected by the Lickorish test | 2-7t+14t^2-17t^3+14t^4-7t^5+2t^6 Seifert matrix of 10_65
| 2 | 63 First homology of the double branched cover of 10_65 Z/63 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_66 | 3 detected by the signature | 3-9t+16t^2-19t^3+16t^4-9t^5+3t^6 Seifert matrix of 10_66
| 1 Generator of the Alexander module (1,0,0,0,1,0) the Blanchfield form on it 6t^-2-15t^-1+20-15t+6t^2 | 75 First homology of the double branched cover of 10_66 Z/75 | -6 | 6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_67 | 2 detected by the Lickorish test | -4+16t-23t^2+16t^3-4t^4 Seifert matrix of 10_67
| 1 Generator of the Alexander module (0,0,1,0) the Blanchfield form on it 2t^-2-8t^-1+12-8t+2t^2 | 63 First homology of the double branched cover of 10_67 Z/63 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_68 | 1 detected by an unknotting move | 4-14t+21t^2-14t^3+4t^4 Seifert matrix of 10_68
| 1 Generator of the Alexander module (0,4-6t+4t^2,0,-3+4t-2t^2) the Blanchfield form on it -4t^-1+8-4t | 57 First homology of the double branched cover of 10_68 Z/57 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_69 | 2 detected by the Lickorish test | 1-7t+21t^2-29t^3+21t^4-7t^5+t^6 Seifert matrix of 10_69
| 1 or 2 | 87 First homology of the double branched cover of 10_69 Z/87 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_70 | 1 detected by an unknotting move | 1-7t+16t^2-19t^3+16t^4-7t^5+t^6 Seifert matrix of 10_70
| 1 Generator of the Alexander module (0,0,1,0,0,0) the Blanchfield form on it -t^-2+7t^-1-13+7t-t^2 | 67 First homology of the double branched cover of 10_70 Z/67 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_71 | 1 detected by an unknotting move | -1+7t-18t^2+25t^3-18t^4+7t^5-t^6 Seifert matrix of 10_71
| 1 Generator of the Alexander module (0,0,0,0,0,1) the Blanchfield form on it -t^-2+3t^-1-5+3t-t^2 | 77 First homology of the double branched cover of 10_71 Z/77 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_72 | 2 detected by the signature | -2+9t-16t^2+19t^3-16t^4+9t^5-2t^6 Seifert matrix of 10_72
| 1 Generator of the Alexander module (0,0,1+t-t^2,1-t,0,0) the Blanchfield form on it -2t^-2+7t^-1-8+7t-2t^2 | 73 First homology of the double branched cover of 10_72 Z/73 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_73 | 1 detected by an unknotting move | 1-7t+20t^2-27t^3+20t^4-7t^5+t^6 Seifert matrix of 10_73
| 1 Generator of the Alexander module (0,0,0,0,1,0) the Blanchfield form on it -1 | 83 First homology of the double branched cover of 10_73 Z/83 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_74 | 2 detected by the Nakanishi index | -4+16t-23t^2+16t^3-4t^4 Seifert matrix of 10_74
| 2 | 63 First homology of the double branched cover of 10_74 Z/21+Z/3 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_75 | 2 detected by the Nakanishi index | -1+7t-19t^2+27t^3-19t^4+7t^5-t^6 Seifert matrix of 10_75
| 2 | 81 First homology of the double branched cover of 10_75 Z/27+Z/3 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_76 | 2 detected by the signature | -2+7t-12t^2+15t^3-12t^4+7t^5-2t^6 Seifert matrix of 10_76
| 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 | 57 First homology of the double branched cover of 10_76 Z/57 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_77 | 1 detected by an unknotting move | 2-7t+14t^2-17t^3+14t^4-7t^5+2t^6 Seifert matrix of 10_77
| 1 Generator of the Alexander module (0,0,1,0,1,0) the Blanchfield form on it -3t^-2+9t^-1-13+9t-3t^2 | 63 First homology of the double branched cover of 10_77 Z/63 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_78 | 2 detected by the signature | -1+7t-16t^2+21t^3-16t^4+7t^5-t^6 Seifert matrix of 10_78
| 1 Generator of the Alexander module (0,1,1,0,0,0) the Blanchfield form on it 2t^-1-3+2t | 69 First homology of the double branched cover of 10_78 Z/69 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_79 | 1 detected by an unknotting move | 1-3t+7t^2-12t^3+15t^4-12t^5+7t^6-3t^7+t^8 Seifert matrix of 10_79
| 1 Generator of the Alexander module (0,0,-t,1,0,0,0,0) the Blanchfield form on it t^-3-2t^-2+5t^-1-6+5t-2t^2+t^3 | 61 First homology of the double branched cover of 10_79 Z/61 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_80 | 3 detected by the signature | 3-9t+15t^2-17t^3+15t^4-9t^5+3t^6 Seifert matrix of 10_80
| 1 Generator of the Alexander module (1,0,0,0,0,0) the Blanchfield form on it 2t^-2-4t^-1+5-4t+2t^2 | 71 First homology of the double branched cover of 10_80 Z/71 | -6 | 6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_81 | 1 detected by an unknotting move | -1+8t-20t^2+27t^3-20t^4+8t^5-t^6 Seifert matrix of 10_81
| 1 Generator of the Alexander module (0,0,t,0,-t,1) the Blanchfield form on it t^-2-7t^-1+10-7t+t^2 | 85 First homology of the double branched cover of 10_81 Z/85 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_82 | 1 detected by an unknotting move | -1+4t-8t^2+12t^3-13t^4+12t^5-8t^6+4t^7-t^8 Seifert matrix of 10_82
| 1 Generator of the Alexander module (0,0,0,0,0,0,0,1) the Blanchfield form on it -t^-3+4t^-2-8t^-1+11-8t+4t^2-t^3 | 63 First homology of the double branched cover of 10_82 Z/63 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_83 | 1 detected by an unknotting move | 2-9t+19t^2-23t^3+19t^4-9t^5+2t^6 Seifert matrix of 10_83
| 1 Generator of the Alexander module (0,0,0,1,0,0) the Blanchfield form on it t^-3-5t^-2+11t^-1-14+11t-5t^2+t^3 | 83 First homology of the double branched cover of 10_83 Z/83 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_84 | 1 detected by an unknotting move | 2-9t+20t^2-25t^3+20t^4-9t^5+2t^6 Seifert matrix of 10_84
| 1 Generator of the Alexander module (1-t,0,0,0,2-t,0) the Blanchfield form on it 2t^-2-7t^-1+10-7t+2t^2 | 87 First homology of the double branched cover of 10_84 Z/87 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_85 | 2 detected by the signature | 1-4t+8t^2-10t^3+11t^4-10t^5+8t^6-4t^7+t^8 Seifert matrix of 10_85
| 1 Generator of the Alexander module (0,0,0,1,0,0,0,0) the Blanchfield form on it -t^-3+4t^-2-8t^-1+9-8t+4t^2-t^3 | 57 First homology of the double branched cover of 10_85 Z/57 | 4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_86 | 2 detected by the Lickorish test | -2+9t-19t^2+25t^3-19t^4+9t^5-2t^6 Seifert matrix of 10_86
| 1 Generator of the Alexander module (0,-t,t,0,1,0) the Blanchfield form on it -t^-2+3t^-1-4+3t-t^2 | 85 First homology of the double branched cover of 10_86 Z/85 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_87 | 1 detected by an unknotting move | -2+9t-18t^2+23t^3-18t^4+9t^5-2t^6 Seifert matrix of 10_87
| 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 | 81 First homology of the double branched cover of 10_87 Z/81 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_88 | 1 detected by an unknotting move | -1+8t-24t^2+35t^3-24t^4+8t^5-t^6 Seifert matrix of 10_88
| 1 Generator of the Alexander module (0,0,0,1,0,0) the Blanchfield form on it t^-2-5t^-1+9-5t+t^2 | 101 First homology of the double branched cover of 10_88 Z/101 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_89 | 2 detected by the Lickorish test | 1-8t+24t^2-33t^3+24t^4-8t^5+t^6 Seifert matrix of 10_89
| 1 Generator of the Alexander module (0,0,0,1,0,0) the Blanchfield form on it t^-1-3+t | 99 First homology of the double branched cover of 10_89 Z/99 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_90 | 1 detected by an unknotting move | -2+8t-17t^2+23t^3-17t^4+8t^5-2t^6 Seifert matrix of 10_90
| 1 Generator of the Alexander module (0,0,0,0,0,1) the Blanchfield form on it t^-3-4t^-2+9t^-1-12+9t-4t^2+t^3 | 77 First homology of the double branched cover of 10_90 Z/77 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_91 | 1 detected by an unknotting move | 1-4t+9t^2-14t^3+17t^4-14t^5+9t^6-4t^7+t^8 Seifert matrix of 10_91
| 1 Generator of the Alexander module (0,1,0,-t,-t,0,-t-2t^4,0) the Blanchfield form on it -9t^-3+30t^-2-64t^-1+85-64t+30t^2-9t^3 | 73 First homology of the double branched cover of 10_91 Z/73 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_92 | 2 detected by the signature | -2+10t-20t^2+25t^3-20t^4+10t^5-2t^6 Seifert matrix of 10_92
| 1 Generator of the Alexander module (t,0,0,0,1,0) the Blanchfield form on it 3t^-3-17t^-2+38t^-1-48+38t-17t^2+3t^3 | 89 First homology of the double branched cover of 10_92 Z/89 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_93 | 1 detected by an unknotting move | 2-8t+15t^2-17t^3+15t^4-8t^5+2t^6 Seifert matrix of 10_93
| 1 Generator of the Alexander module (0,-t,0,0,1+t^2,0) the Blanchfield form on it -2t^-2+8t^-1-13+8t-2t^2 | 67 First homology of the double branched cover of 10_93 Z/67 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_94 | 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 10_94
| 1 Generator of the Alexander module (0,0,0,0,0,1,0,0) the Blanchfield form on it -t^-3+4t^-2-8t^-1+11-8t+4t^2-t^3 | 71 First homology of the double branched cover of 10_94 Z/71 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_95 | 1 detected by an unknotting move | 2-9t+21t^2-27t^3+21t^4-9t^5+2t^6 Seifert matrix of 10_95
| 1 Generator of the Alexander module (0,0,0,0,1,0) the Blanchfield form on it -1 | 91 First homology of the double branched cover of 10_95 Z/91 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_96 | 1 detected by an unknotting move | -1+7t-22t^2+33t^3-22t^4+7t^5-t^6 Seifert matrix of 10_96
| 1 or 2 | 93 First homology of the double branched cover of 10_96 Z/93 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_97 | 2 detected by the Lickorish test | -5+22t-33t^2+22t^3-5t^4 Seifert matrix of 10_97
| 1 Generator of the Alexander module (0,-1,1,1) the Blanchfield form on it -3t^-1+8-3t | 87 First homology of the double branched cover of 10_97 Z/87 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_98 | 2 detected by the Nakanishi index | -2+9t-18t^2+23t^3-18t^4+9t^5-2t^6 Seifert matrix of 10_98
| 2 | 81 First homology of the double branched cover of 10_98 Z/27+Z/3 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_99 | 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 10_99
| 2 | 81 First homology of the double branched cover of 10_99 Z/9+Z/9 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_100 | 2 detected by the signature | 1-4t+9t^2-12t^3+13t^4-12t^5+9t^6-4t^7+t^8 Seifert matrix of 10_100
| 1 Generator of the Alexander module (0,0,0,-1+t,0,0,1,2-t) the Blanchfield form on it -t^-3+3t^-2-6t^-1+7-6t+3t^2-t^3 | 65 First homology of the double branched cover of 10_100 Z/65 | 4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_101 | 2 detected by the signature | 7-21t+29t^2-21t^3+7t^4 Seifert matrix of 10_101
| 1 or 2 | 85 First homology of the double branched cover of 10_101 Z/85 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_102 | 1 detected by an unknotting move | -2+8t-16t^2+21t^3-16t^4+8t^5-2t^6 Seifert matrix of 10_102
| 1 Generator of the Alexander module (0,0,0,0,1,0) the Blanchfield form on it t^-3-4t^-2+8t^-1-10+8t-4t^2+t^3 | 73 First homology of the double branched cover of 10_102 Z/73 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_103 | 3 detected by the new u==2 criterion | 2-8t+17t^2-21t^3+17t^4-8t^5+2t^6 Seifert matrix of 10_103
| 2 | 75 First homology of the double branched cover of 10_103 Z/15+Z/5 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_104 | 1 detected by an unknotting move | 1-4t+9t^2-15t^3+19t^4-15t^5+9t^6-4t^7+t^8 Seifert matrix of 10_104
| 1 Generator of the Alexander module (0,0,0,0,1,0,0,-1) the Blanchfield form on it -t^-2+3t^-1-7+3t-t^2 | 77 First homology of the double branched cover of 10_104 Z/77 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_105 | 2 detected by the Lickorish test | 1-8t+22t^2-29t^3+22t^4-8t^5+t^6 Seifert matrix of 10_105
| 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 | 91 First homology of the double branched cover of 10_105 Z/91 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_106 | 2 detected by the Lickorish test | -1+4t-9t^2+15t^3-17t^4+15t^5-9t^6+4t^7-t^8 Seifert matrix of 10_106
| 1 Generator of the Alexander module (0,0,0,1,0,0,0,0) the Blanchfield form on it -t^-3+4t^-2-8t^-1+11-8t+4t^2-t^3 | 75 First homology of the double branched cover of 10_106 Z/75 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_107 | 1 detected by an unknotting move | -1+8t-22t^2+31t^3-22t^4+8t^5-t^6 Seifert matrix of 10_107
| 1 Generator of the Alexander module (0,-6,3,1,-2t^2,-11-t-3t^2) the Blanchfield form on it -127t^-2-8t^-1-30-8t-127t^2 | 93 First homology of the double branched cover of 10_107 Z/93 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_108 | 2 detected by the Lickorish test | 2-8t+14t^2-15t^3+14t^4-8t^5+2t^6 Seifert matrix of 10_108
| 1 Generator of the Alexander module (-15+120t-268t^2+162t^3+198t^4-864t^5+1218t^6-1320t^7+768t^8-192t^9,24-186t+84t^2+336t^3-1108t^4+1516t^5-1720t^6+1036t^7-264t^8,5-42t+96t^2-142t^3+154t^4-124t^5+58t^6-12t^7,-9+70t-36t^2-114t^3+394t^4-544t^5+622t^6-376t^7+96t^8,6t-48t^2-72t^3+348t^4-780t^5+960t^6-996t^7+576t^8-144t^9,-10+84t-192t^2+2 the Blanchfield form on it x | 63 First homology of the double branched cover of 10_108 Z/63 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_109 | 2 detected by the Lickorish test | 1-4t+10t^2-17t^3+21t^4-17t^5+10t^6-4t^7+t^8 Seifert matrix of 10_109
| 1 Generator of the Alexander module (0,0,0,0,0,1,0,0) the Blanchfield form on it -t^-1+1-t | 85 First homology of the double branched cover of 10_109 Z/85 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_110 | 1 detected by an unknotting move | 1-8t+20t^2-25t^3+20t^4-8t^5+t^6 Seifert matrix of 10_110
| 1 Generator of the Alexander module (0,1-6t+10t^2-12t^3+2t^4+9t^5-14t^6+11t^7-5t^8+t^9,t-2t^2+5t^3-4t^4+3t^5-t^6,1-4t+4t^2+3t^3-18t^4+28t^5-26t^6+16t^7-6t^8+t^9,-4+5t-8t^2-t^3+10t^4-14t^5+11t^6-5t^7+t^8,0) the Blanchfield form on it x | 83 First homology of the double branched cover of 10_110 Z/83 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_111 | 2 detected by the signature | -2+9t-17t^2+21t^3-17t^4+9t^5-2t^6 Seifert matrix of 10_111
| 1 Generator of the Alexander module (-2t+2t^2-2t^3,0,2-2t+2t^2,3-2t+2t^2,0,2-2t+2t^2) the Blanchfield form on it -2t^-2+8t^-1-11+8t-2t^2 | 77 First homology of the double branched cover of 10_111 Z/77 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_112 | 1 detected by an unknotting move | -1+5t-11t^2+17t^3-19t^4+17t^5-11t^6+5t^7-t^8 Seifert matrix of 10_112
| 1 Generator of the Alexander module (0,0,1,-t^4,0,-t,0,0) the Blanchfield form on it -t^-2+4t^-1-6+4t-t^2 | 87 First homology of the double branched cover of 10_112 Z/87 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_113 | 1 detected by an unknotting move | 2-11t+26t^2-33t^3+26t^4-11t^5+2t^6 Seifert matrix of 10_113
| 1 Generator of the Alexander module (3-4t+2t^2,0,2,0,0,0) the Blanchfield form on it -69t^-3+380t^-2-899t^-1+1142-899t+380t^2-69t^3 | 111 First homology of the double branched cover of 10_113 Z/111 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_114 | 1 detected by an unknotting move | -2+10t-21t^2+27t^3-21t^4+10t^5-2t^6 Seifert matrix of 10_114
| 1 Generator of the Alexander module (0,0,1,1,t,1-t) the Blanchfield form on it 2t^-2-7t^-1+8-7t+2t^2 | 93 First homology of the double branched cover of 10_114 Z/93 | 0 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_115 | 2 detected by A(F_2) | -1+9t-26t^2+37t^3-26t^4+9t^5-t^6 Seifert matrix of 10_115
| 2 | 109 First homology of the double branched cover of 10_115 Z/109 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_116 | 2 detected by the Lickorish test | -1+5t-12t^2+19t^3-21t^4+19t^5-12t^6+5t^7-t^8 Seifert matrix of 10_116
| 1 Generator of the Alexander module (0,0,0,0,0,0,0,1) the Blanchfield form on it t^-3-4t^-2+8t^-1-11+8t-4t^2+t^3 | 95 First homology of the double branched cover of 10_116 Z/95 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_117 | 1 detected by an unknotting move | 2-10t+24t^2-31t^3+24t^4-10t^5+2t^6 Seifert matrix of 10_117
| 1 Generator of the Alexander module (0,0,0,1,0,0) the Blanchfield form on it -t^-1+1-t | 103 First homology of the double branched cover of 10_117 Z/103 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_118 | 1 detected by an unknotting move | 1-5t+12t^2-19t^3+23t^4-19t^5+12t^6-5t^7+t^8 Seifert matrix of 10_118
| 1 Generator of the Alexander module (0,-1,0,t,1,0,0,t) the Blanchfield form on it -t^-3+4t^-2-8t^-1+9-8t+4t^2-t^3 | 97 First homology of the double branched cover of 10_118 Z/97 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_119 | 1 detected by an unknotting move | -2+10t-23t^2+31t^3-23t^4+10t^5-2t^6 Seifert matrix of 10_119
| 1 Generator of the Alexander module (0,0,4t-2t^2,t,1,t) the Blanchfield form on it -2t^-2+6t^-1-9+6t-2t^2 | 101 First homology of the double branched cover of 10_119 Z/101 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_120 | 2 detected by the signature | 8-26t+37t^2-26t^3+8t^4 Seifert matrix of 10_120
| 1 Generator of the Alexander module (0,0,1-t,t) the Blanchfield form on it -28t^-2+95t^-1-136+95t-28t^2 | 105 First homology of the double branched cover of 10_120 Z/105 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_121 | 2 detected by the Lickorish test | 2-11t+27t^2-35t^3+27t^4-11t^5+2t^6 Seifert matrix of 10_121
| 1 Generator of the Alexander module (0,1,0,0,1,0) the Blanchfield form on it -2t^-1+3-2t | 115 First homology of the double branched cover of 10_121 Z/115 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_122 | 2 detected by the Lickorish test | -2+11t-24t^2+31t^3-24t^4+11t^5-2t^6 Seifert matrix of 10_122
| 2 | 105 First homology of the double branched cover of 10_122 Z/105 | 0 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_123 | 2 detected by the Nakanishi index | 1-6t+15t^2-24t^3+29t^4-24t^5+15t^6-6t^7+t^8 Seifert matrix of 10_123
| 2 | 121 First homology of the double branched cover of 10_123 Z/11+Z/11 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_124 | 4 detected by the signature | -1+t-t^3+t^4-t^5+t^7-t^8 Seifert matrix of 10_124
| 1 Generator of the Alexander module (0,1,0,0,0,0,0,0) the Blanchfield form on it -t^-3+t^-2-t^-1+1-t+t^2-t^3 | 1 First homology of the double branched cover of 10_124 0 | -8 | 8 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_125 | 1 detected by an unknotting move | 1-2t+2t^2-t^3+2t^4-2t^5+t^6 Seifert matrix of 10_125
| 1 Generator of the Alexander module (1,0,0,0,1,0) the Blanchfield form on it -t^-2+t^-1+t-t^2 | 11 First homology of the double branched cover of 10_125 Z/11 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_126 | 1 detected by an unknotting move | 1-2t+4t^2-5t^3+4t^4-2t^5+t^6 Seifert matrix of 10_126
| 1 Generator of the Alexander module (-t,0,0,1,0,0) the Blanchfield form on it t^-2-2t^-1+2-2t+t^2 | 19 First homology of the double branched cover of 10_126 Z/19 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_127 | 2 detected by the signature | -1+4t-6t^2+7t^3-6t^4+4t^5-t^6 Seifert matrix of 10_127
| 1 Generator of the Alexander module (-t,0,0,1,0,0) the Blanchfield form on it -t^-2+2t^-1-2+2t-t^2 | 29 First homology of the double branched cover of 10_127 Z/29 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_128 | 3 detected by the signature | 2-3t+t^2+t^3+t^4-3t^5+2t^6 Seifert matrix of 10_128
| 1 Generator of the Alexander module (0,1,0,-1,1,0) the Blanchfield form on it 2t^-2-5t^-1+7-5t+2t^2 | 11 First homology of the double branched cover of 10_128 Z/11 | -6 | 6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_129 | 1 detected by an unknotting move | 2-6t+9t^2-6t^3+2t^4 Seifert matrix of 10_129
| 1 Generator of the Alexander module (t,0,0,1) the Blanchfield form on it 2t^-1-2+2t | 25 First homology of the double branched cover of 10_129 Z/25 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_130 | 1 detected by an unknotting move | 2-4t+5t^2-4t^3+2t^4 Seifert matrix of 10_130
| 1 Generator of the Alexander module (-t,0,0,1) the Blanchfield form on it 2t^-1-4+2t | 17 First homology of the double branched cover of 10_130 Z/17 | 0 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_131 | 1 detected by an unknotting move | -2+8t-11t^2+8t^3-2t^4 Seifert matrix of 10_131
| 1 Generator of the Alexander module (0,0,1,-1) the Blanchfield form on it -2t^-1+3-2t | 31 First homology of the double branched cover of 10_131 Z/31 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_132 | 1 detected by an unknotting move | 1-t+t^2-t^3+t^4 Seifert matrix of 10_132
| 1 Generator of the Alexander module (-1,0,1,0) the Blanchfield form on it t^-1-2+t | 5 First homology of the double branched cover of 10_132 Z/5 | 0 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_133 | 1 detected by an unknotting move | -1+5t-7t^2+5t^3-t^4 Seifert matrix of 10_133
| 1 Generator of the Alexander module (0,0,0,1) the Blanchfield form on it 1 | 19 First homology of the double branched cover of 10_133 Z/19 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_134 | 3 detected by the signature | 2-4t+4t^2-3t^3+4t^4-4t^5+2t^6 Seifert matrix of 10_134
| 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 | 23 First homology of the double branched cover of 10_134 Z/23 | -6 | 6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_135 | 1 detected by an unknotting move | 3-9t+13t^2-9t^3+3t^4 Seifert matrix of 10_135
| 1 Generator of the Alexander module (0,0,1,0) the Blanchfield form on it -t^-2+3t^-1-4+3t-t^2 | 37 First homology of the double branched cover of 10_135 Z/37 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_136 | 1 detected by an unknotting move | -1+4t-5t^2+4t^3-t^4 Seifert matrix of 10_136
| 1 Generator of the Alexander module (0,0,0,1) the Blanchfield form on it t^-1-2+t | 15 First homology of the double branched cover of 10_136 Z/15 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_137 | 1 detected by an unknotting move | 1-6t+11t^2-6t^3+t^4 Seifert matrix of 10_137
| 1 Generator of the Alexander module (0,1,-2,0) the Blanchfield form on it -t^-1+4-t | 25 First homology of the double branched cover of 10_137 Z/25 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_138 | 1 detected by an unknotting move | 1-5t+8t^2-7t^3+8t^4-5t^5+t^6 Seifert matrix of 10_138
| 1 Generator of the Alexander module (0,0,0,0,0,1) the Blanchfield form on it -2t^-1+5-2t | 35 First homology of the double branched cover of 10_138 Z/35 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_139 | 3 detected by the signature | 1-t+2t^3-3t^4+2t^5-t^7+t^8 Seifert matrix of 10_139
| 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 | 3 First homology of the double branched cover of 10_139 Z/3 | -6 | 6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_140 | 2 detected by A(F_2) | 1-2t+3t^2-2t^3+t^4 Seifert matrix of 10_140
| 2 | 9 First homology of the double branched cover of 10_140 Z/9 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_141 | 1 detected by an unknotting move | -1+3t-4t^2+5t^3-4t^4+3t^5-t^6 Seifert matrix of 10_141
| 1 Generator of the Alexander module (-t,0,1,1,0,1) the Blanchfield form on it 1 | 21 First homology of the double branched cover of 10_141 Z/21 | 0 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_142 | 3 detected by the signature | 2-3t+2t^2-t^3+2t^4-3t^5+2t^6 Seifert matrix of 10_142
| 2 | 15 First homology of the double branched cover of 10_142 Z/15 | -6 | 6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_143 | 1 detected by an unknotting move | 1-3t+6t^2-7t^3+6t^4-3t^5+t^6 Seifert matrix of 10_143
| 1 Generator of the Alexander module (0,0,1,0,0,0) the Blanchfield form on it -1 | 27 First homology of the double branched cover of 10_143 Z/27 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_144 | 2 detected by the Lickorish test | -3+10t-13t^2+10t^3-3t^4 Seifert matrix of 10_144
| 2 | 39 First homology of the double branched cover of 10_144 Z/39 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_145 | 1 detected by an unknotting move | 1+t-3t^2+t^3+t^4 Seifert matrix of 10_145
| 1 Generator of the Alexander module (0,1,t,0) the Blanchfield form on it t^-1-2+t | 3 First homology of the double branched cover of 10_145 Z/3 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_146 | 1 detected by an unknotting move | 2-8t+13t^2-8t^3+2t^4 Seifert matrix of 10_146
| 1 Generator of the Alexander module (7t+14t^2-21t^3+7t^4,-1-2t+3t^2-t^3,54t+60t^2-162t^3+94t^4-16t^5,2t-2t^2-6t^3+7t^4-2t^5) the Blanchfield form on it 1425t^-6-12200t^-5+35579t^-4-13578t^-3-171458t^-2+492598t^-1-664732+492598t-171458t^2-13578t^3+35579t^4-12200t^5+1425t^6 | 33 First homology of the double branched cover of 10_146 Z/33 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_147 | 1 detected by an unknotting move | -2+7t-9t^2+7t^3-2t^4 Seifert matrix of 10_147
| 1 Generator of the Alexander module (1+2t-2t^2,-1-2t+t^2,0,-1-4t+2t^2) the Blanchfield form on it -2t^-1+3-2t | 27 First homology of the double branched cover of 10_147 Z/27 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_148 | 1 detected by an unknotting move | 1-3t+7t^2-9t^3+7t^4-3t^5+t^6 Seifert matrix of 10_148
| 1 Generator of the Alexander module (0,0,t,1,-1,1) the Blanchfield form on it t^-2-3t^-1+4-3t+t^2 | 31 First homology of the double branched cover of 10_148 Z/31 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_149 | 2 detected by the signature | -1+5t-9t^2+11t^3-9t^4+5t^5-t^6 Seifert matrix of 10_149
| 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 | 41 First homology of the double branched cover of 10_149 Z/41 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_150 | 2 detected by the signature | -1+4t-6t^2+7t^3-6t^4+4t^5-t^6 Seifert matrix of 10_150
| 1 Generator of the Alexander module (0,0,1,0,0,-t) the Blanchfield form on it -t^-2+3t^-1-2+3t-t^2 | 29 First homology of the double branched cover of 10_150 Z/29 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_151 | 1 detected by an unknotting move | 1-4t+10t^2-13t^3+10t^4-4t^5+t^6 Seifert matrix of 10_151
| 1 Generator of the Alexander module (0,0,1,0,0,0) the Blanchfield form on it -t^-1+1-t | 43 First homology of the double branched cover of 10_151 Z/43 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_152 | 3 detected by the signature | 1-t-t^2+4t^3-5t^4+4t^5-t^6-t^7+t^8 Seifert matrix of 10_152
| 1 Generator of the Alexander module (0,0,0,0,0,0,0,1) the Blanchfield form on it t^-3-t^-2+1-t^2+t^3 | 11 First homology of the double branched cover of 10_152 Z/11 | -6 | 6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_153 | 1 detected by an unknotting move | 1-t-t^2+3t^3-t^4-t^5+t^6 Seifert matrix of 10_153
| 1 Generator of the Alexander module (1,0,0,0,0,0) the Blanchfield form on it 2t^-1-3+2t | 1 First homology of the double branched cover of 10_153 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_154 | 2 detected by the signature | 1-4t^2+7t^3-4t^4+t^6 Seifert matrix of 10_154
| 1 Generator of the Alexander module (0,1,0,0,0,t) the Blanchfield form on it t^-2+2t^-1-4+2t+t^2 | 13 First homology of the double branched cover of 10_154 Z/13 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_155 | 2 detected by the Nakanishi index | -1+3t-5t^2+7t^3-5t^4+3t^5-t^6 Seifert matrix of 10_155
| 2 | 25 First homology of the double branched cover of 10_155 Z/5+Z/5 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_156 | 1 detected by an unknotting move | 1-4t+8t^2-9t^3+8t^4-4t^5+t^6 Seifert matrix of 10_156
| 1 Generator of the Alexander module (0,0,1,0,0,0) the Blanchfield form on it -1 | 35 First homology of the double branched cover of 10_156 Z/35 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_157 | 2 detected by the Nakanishi index | -1+6t-11t^2+13t^3-11t^4+6t^5-t^6 Seifert matrix of 10_157
| 2 | 49 First homology of the double branched cover of 10_157 Z/7+Z/7 | 4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_158 | 1 detected by an unknotting move | -1+4t-10t^2+15t^3-10t^4+4t^5-t^6 Seifert matrix of 10_158
| 1 Generator of the Alexander module (-t^2-t^4-t^5,2t^4+2t^6+t^7-3t^8-2t^9,t^2+t^4+t^5,-1-t+t^2+2t^3-t^4+2t^6-4t^7-4t^8+4t^9+4t^10,-t^5-t^6,-t^2+2t^3+2t^5+2t^6) the Blanchfield form on it x | 45 First homology of the double branched cover of 10_158 Z/45 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_159 | 1 detected by an unknotting move | 1-4t+9t^2-11t^3+9t^4-4t^5+t^6 Seifert matrix of 10_159
| 1 Generator of the Alexander module (0,0,1,0,0,0) the Blanchfield form on it 1 | 39 First homology of the double branched cover of 10_159 Z/39 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_160 | 2 detected by the signature | -1+4t-4t^2+3t^3-4t^4+4t^5-t^6 Seifert matrix of 10_160
| 1 or 2 | 21 First homology of the double branched cover of 10_160 Z/21 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_161 | 2 detected by the signature | 1-2t^2+3t^3-2t^4+t^6 Seifert matrix of 10_161
| 1 Generator of the Alexander module (0,0,1,0,0,t) the Blanchfield form on it -t^-2+3t^-1-4+3t-t^2 | 5 First homology of the double branched cover of 10_161 Z/5 | -4 | 4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_162 | 1 detected by an unknotting move | -3+9t-11t^2+9t^3-3t^4 Seifert matrix of 10_162
| 1 or 2 | 35 First homology of the double branched cover of 10_162 Z/35 | 2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_163 | 2 detected by the Lickorish test | 1-5t+12t^2-15t^3+12t^4-5t^5+t^6 Seifert matrix of 10_163
| 2 | 51 First homology of the double branched cover of 10_163 Z/51 | -2 | 2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_164 | 1 detected by an unknotting move | 3-11t+17t^2-11t^3+3t^4 Seifert matrix of 10_164
| 1 Generator of the Alexander module (0,4t,2,-1+2t) the Blanchfield form on it 3t^-1-5+3t | 45 First homology of the double branched cover of 10_164 Z/45 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

10_165 | 2 detected by the Lickorish test | -2+10t-15t^2+10t^3-2t^4 Seifert matrix of 10_165
| 1 Generator of the Alexander module (0,0,1,0) the Blanchfield form on it 2t^-1-4+2t | 39 First homology of the double branched cover of 10_165 Z/39 | 2 | 2 |