| name: | 12n_242
|
| category: | 12 |
| knot_atlas: | NULL |
| alternating: | N |
| name_rank: | 2332 |
| dt_name: | 12n_242 |
| dt_rank: | 2332 |
| dt_notation: | [4, 8, -16, 2, -18, -20, -22, -24, -6, -10, -12, -14] |
| classical_conway_name: | NULL |
| conway_notation: | [7;-2 1;2] |
| two_bridge_notation: | NULL |
| fibered: | Y |
| gauss_notation: | {1, -2, 3, -1, -4, 5, 2, -3, -6, 7, -8, 9, -10, 11, -12, 4, -5, 6, -7, 8, -9, 10, -11, 12} |
| pd_notation: | [[1,5,2,4],[3,9,4,8],[16,6,17,5],[7,3,8,2],[18,10,19,9],[20,12,21,11],[22,14,23,13],[24,16,1,15],[6,18,7,17],[10,20,11,19],[12,22,13,21],[14,24,15,23]] |
| crossing_number: | 12 |
| tetrahedral_census_name: | [3, K3_1, m016] |
| unknotting_number: | 5
|
| three_genus: | 5 |
| crosscap_number: | 2 |
| bridge_index: | 3 |
| braid_index: | 3 |
| braid_length: | NULL |
| braid_notation: | {1,2,2,1,1,2,2,2,2,2,2,2} |
| signature: | -8 |
| nakanishi_index: | 1 |
| super_bridge_index: | NULL |
| thurston_bennequin_number: | [9][-18] |
| arc_index: | 9 |
| polygon_index: | [9,10] |
| tunnel_number: | 1 |
| morse_novikov_number: | 0 |
| alexander_polynomial: | 1-t+t^3-t^4+t^5-t^6+t^7-t^9+t^10 |
| alexander_polynomial_vector: | {0, 10, 1, -1, 0, 1, -1, 1, -1, 1, 0, -1, 1} |
| jones_polynomial: | t^5+ t^7-t^11+ t^12-t^13 |
| jones_polynomial_vector: | {5, 13, 1, 0, 1, 0, 0, 0, -1, 1, -1} |
| conway_polynomial: | 1+12*z^2+31*z^4+27*z^6+9*z^8+z^10 |
| conway_polynomial_vector: | {0, 5, 1, 12, 31, 27, 9, 1} |
| homfly_polynomial_vector: | {0, 5, {5, 7, 9, -11, 3}, {5, 7, 39, -31, 4}, {5, 7, 57, -27, 1}, {5, 6, 36, -9}, {5, 6, 10, -1}, {5, 5, 1}} |
| kauffman_polynomial: | (-3*a^(-14)-11*a^(-12)-9*a^(-10))*z^(0)+(a^(-17)+a^(-15)+11*a^(-13)+11*a^(-11))*z^(1)+(a^(-16)+4*a^(-14)+42*a^(-12)+39*a^(-10))*z^(2)+(-31*a^(-13)-31*a^(-11))*z^(3)+(-a^(-14)-58*a^(-12)-57*a^(-10))*z^(4)+(27*a^(-13)+27*a^(-11))*z^(5)+(36*a^(-12)+36*a^(-10))*z^(6)+(-9*a^(-13)-9*a^(-11))*z^(7)+(-10*a^(-12)-10*a^(-10))*z^(8)+(a^(-13)+a^(-11))*z^(9)+(a^(-12)+a^(-10))*z^(10) |
| kauffman_polynomial_vector: | {0, 10, {-14, -10, -3, 0, -11, 0, -9}, {-17, -11, 1, 0, 1, 0, 11, 0, 11}, {-16, -10, 1, 0, 4, 0, 42, 0, 39}, {-13, -11, -31, 0, -31}, {-14, -10, -1, 0, -58, 0, -57}, {-13, -11, 27, 0, 27}, {-12, -10, 36, 0, 36}, {-13, -11, -9, 0, -9}, {-12, -10, -10, 0, -10}, {-13, -11, 1, 0, 1}, {-12, -10, 1, 0, 1}} |
| a_polynomial: | table of A-polys
|
| smooth_four_genus: | 5 |
| topological_four_genus: | 4
|
| smooth_4d_crosscap_number: | NULL |
| topological_4d_crosscap_number: | NULL |
| smooth_concordance_genus: | 5 |
| topological_concordance_genus: | NULL |
| smooth_concordance_crosscap_number: | NULL |
| topological_concordance_crosscap_number: | NULL |
| algebraic_concordance_order: | infty |
| smooth_concordance_order: | infty |
| topological_concordance_order: | infty |
| ribbon: | NULL |
| determinant: | 1 |
| seifert_matrix: | [[ -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]] |
| rasmussen_invariant: | 10 |
| ozsvath_szabo_tau_invariant: | 5 |
| volume: | 2.828122088 |
| maximum_cusp_volume: | 2.012733281 |
| longitude_translation: | (32.04743701, 0) |
| meridian_translation: | ( 1.750376487 , 0.125609626 ) |
| longitude_length: | 32.04743701 |
| meridian_length: | 1.754877666 |
| other_short_geodesics: | [(35 , -2 , 5.229367635 ), (37 , -2 , 4.695467392 ), (16 , -1 , 4.513549821 ), (17 , -1 , 3.131872788 ), (18 , -1 , 2.324717957 ), (19 , -1 , 2.675666505 ), (20 , -1 , 3.882429672 )] |
| symmetry_type: | reversible |
| full_symmetry_group: | D1 |
| chern_simons_invariant: | 0.236537467 |
| volume_imaginary_part: | 4.669062443 |
| arf_invariant: | 0 |
| turaev_genus: | 1 |
| signature_function: | {{0.1076990118, {0, -1, -2}, 1}, {0.2374458357, {-2, -3, -4}, 1}, {0.4055687721, {-4, -5, -6}, 1}, {0.6510280597, {-6, -7, -8}, 1}}
|
| monodromy: | abcdefghil |
| small_large: | Small |
| positive_braid: | Y |
| positive: | Y |
| strongly_quasipositive: | Y |
| quasipositive: | Y |
| positive_braid_notation: | {1,2,2,1,1,2,2,2,2,2,2,2} |
| positive_pd_notation: | {{1,4,2,5},{3,8,4,9},{16,5,17,6},{7,2,8,3},{18,9,19,10},{20,11,21,12},{22,13,23,14},{24,15,1,16},{6,17,7,18},{10,19,11,20},{12,21,13,22},{14,23,15,24}} |
| strongly_quasipositive_braid_notation: | M{-1,-2,-2,-1,-1,-2,-2,-2,-2,-2,-2,-2} |
| quasipositive_braid_notation: | M{-1,-2,-2,-1,-1,-2,-2,-2,-2,-2,-2,-2} |
| fd_clasp_number: | NULL |
| width: | 18 |
| torsion_numbers: | {{2,{1}}, {3,{1}}, {4,{3,3}}, {5,{1}}, {6,{1}}, {7,{13,13}}, {8,{3,3}}, {9,{1}}} |
| td_clasp_number: | NULL |
| l_space: | Yes |
| nu: | {5,-4} |
| epsilon: | 1 |
| quasi_alternating: | NULL |
| almost_alternating: | |
| adequate: | NULL |
| montesinos_notation: | K(1/2;-2/3;1/7) |
| boundary_slopes: | NULL |
| pretzel_notation: | NULL |
| double_slice_genus: | 10 |
| unknotting_number_algebraic: | 4 |
| khovanov_unreduced_integral_polynomial: | q^(9) + q^(11) + t^(2) q^(13) + t^(3) q^(17) + t^(4) q^(15) + t^(4) q^(17) + t^(5) q^(19) + t^(5) q^(21) + t^(6) q^(19) + t^(7) q^(23) + t^(8) q^(23) + t^(9) q^(27) + t^(3) q^(15) T^(2) + t^(7) q^(21) T^(2) + t^(9) q^(25) T^(2) |
| khovanov_unreduced_integral_vector: | [[0, 1, 0, 9], [0, 1, 0, 11], [0, 1, 2, 13], [0, 1, 3, 17], [0, 1, 4, 15], [0, 1, 4, 17], [0, 1, 5, 19], [0, 1, 5, 21], [0, 1, 6, 19], [0, 1, 7, 23], [0, 1, 8, 23], [0, 1, 9, 27], [2, 1, 3, 15], [2, 1, 7, 21], [2, 1, 9, 25]] |
| khovanov_reduced_integral_polynomial: | q^(10) + t^(2) q^(14) + t^(3) q^(16) + t^(4) q^(16) + t^(5) q^(20) + t^(6) q^(20) + t^(7) q^(22) + t^(8) q^(24) + t^(9) q^(26) |
| khovanov_reduced_integral_vector: | [[0, 1, 0, 10], [0, 1, 2, 14], [0, 1, 3, 16], [0, 1, 4, 16], [0, 1, 5, 20], [0, 1, 6, 20], [0, 1, 7, 22], [0, 1, 8, 24], [0, 1, 9, 26]] |
| khovanov_reduced_rational_polynomial: | q^(10) + t^(2) q^(14) + t^(3) q^(16) + t^(4) q^(16) + t^(5) q^(20) + t^(6) q^(20) + t^(7) q^(22) + t^(8) q^(24) + t^(9) q^(26) |
| khovanov_reduced_rational_vector: | [[1, 1, 0, 10], [1, 1, 2, 14], [1, 1, 3, 16], [1, 1, 4, 16], [1, 1, 5, 20], [1, 1, 6, 20], [1, 1, 7, 22], [1, 1, 8, 24], [1, 1, 9, 26]] |
| khovanov_reduced_mod2_polynomial: | q^(10) + t^(2) q^(14) + t^(3) q^(16) + t^(4) q^(16) + t^(5) q^(20) + t^(6) q^(20) + t^(7) q^(22) + t^(8) q^(24) + t^(9) q^(26) |
| khovanov_reduced_mod2_vector: | [[2, 1, 0, 10], [2, 1, 2, 14], [2, 1, 3, 16], [2, 1, 4, 16], [2, 1, 5, 20], [2, 1, 6, 20], [2, 1, 7, 22], [2, 1, 8, 24], [2, 1, 9, 26]] |
| khovanov_odd_integral_polynomial: | q^(10) + t^(2) q^(14) + t^(7) q^(22) + t^(8) q^(24) + t^(9) q^(26) + t^(4) q^(16) T^(2) + t^(6) q^(20) T^(2) + t^(5) q^(18) T^(3) |
| khovanov_odd_integral_vector: | [[0, 1, 0, 10], [0, 1, 2, 14], [0, 1, 7, 22], [0, 1, 8, 24], [0, 1, 9, 26], [2, 1, 4, 16], [2, 1, 6, 20], [3, 1, 5, 18]] |
| khovanov_odd_rational_polynomial: | q^(10) + t^(2) q^(14) + t^(7) q^(22) + t^(8) q^(24) + t^(9) q^(26) |
| khovanov_odd_rational_vector: | [[1, 1, 0, 10], [1, 1, 2, 14], [1, 1, 7, 22], [1, 1, 8, 24], [1, 1, 9, 26]] |
| khovanov_odd_mod2_polynomial: | q^(10) + t^(2) q^(14) + t^(3) q^(16) + t^(4) q^(16) + t^(5) q^(20) + t^(6) q^(20) + t^(7) q^(22) + t^(8) q^(24) + t^(9) q^(26) |
| khovanov_odd_mod2_vector: | [[2, 1, 0, 10], [2, 1, 2, 14], [2, 1, 3, 16], [2, 1, 4, 16], [2, 1, 5, 20], [2, 1, 6, 20], [2, 1, 7, 22], [2, 1, 8, 24], [2, 1, 9, 26]] |
| hfk_polynomial: | 1a^(-5)m^(-10)+ 1a^(-4)m^(-9)+ 1a^(-2)m^(-6)+ 1a^(-1)m^(-5)+ 1a^(0)m^(-4)+ 1a^(1)m^(-3)+ 1a^(2)m^(-2)+ 1a^(4)m^(-1)+ 1a^(5)m^(0) |
| hfk_polynomial_vector: | [1,-5,-10;1,-4,-9;1,-2,-6;1,-1,-5;1,0,-4;1,1,-3;1,2,-2;1,4,-1;1,5,0] |
| mosaic_tile_number: | { 7 , 29 } |
| ropelength: | 83.71441 |
| homfly_polynomial: | (9*v^10-11*v^12+3*v^14)+(39*v^10-31*v^12+4*v^14)*z^2+(57*v^10-27*v^12+v^14)*z^4+(36*v^10-9*v^12)*z^6+(10*v^10-v^12)*z^8+v^10*z^10 |
| grid_notation: | [[1,1],[1,4],[2,2],[2,5],[3,3],[3,7],[4,4],[4,8],[5,5],[5,9],[6,1],[6,6],[7,2],[7,7],[8,3],[8,8],[9,6],[9,9]] |
