| Min(phi) over symmetries of the knot is: [-3,-2,0,1,1,3,-1,1,1,3,4,1,0,2,2,0,0,1,0,0,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.356'] |
| Arrow polynomial of the knot is: 8*K1**3 - 2*K1**2 - 8*K1*K2 - 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.356', '6.596'] |
| Outer characteristic polynomial of the knot is: t^7+66t^5+46t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.356'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**2*K2**4 + 352*K1**2*K2**3 - 1984*K1**2*K2**2 + 1096*K1**2*K2 - 16*K1**2*K3**2 - 972*K1**2 + 672*K1*K2**3*K3 + 2008*K1*K2*K3 + 224*K1*K3*K4 + 56*K1*K4*K5 - 192*K2**6 + 288*K2**4*K4 - 920*K2**4 - 368*K2**2*K3**2 - 160*K2**2*K4**2 + 664*K2**2*K4 - 432*K2**2 + 96*K2*K3*K5 + 56*K2*K4*K6 - 16*K3**4 + 32*K3**2*K6 - 692*K3**2 - 330*K4**2 - 40*K5**2 - 24*K6**2 + 1048 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.356'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.10511', 'vk6.10518', 'vk6.10582', 'vk6.10597', 'vk6.10769', 'vk6.10786', 'vk6.10886', 'vk6.10895', 'vk6.17679', 'vk6.17691', 'vk6.17726', 'vk6.17738', 'vk6.24285', 'vk6.24297', 'vk6.24760', 'vk6.25217', 'vk6.30192', 'vk6.30199', 'vk6.30261', 'vk6.30276', 'vk6.30388', 'vk6.30405', 'vk6.30655', 'vk6.30748', 'vk6.36527', 'vk6.36938', 'vk6.43617', 'vk6.43633', 'vk6.43719', 'vk6.43737', 'vk6.52735', 'vk6.52845', 'vk6.60351', 'vk6.60361', 'vk6.60631', 'vk6.60966', 'vk6.63448', 'vk6.63455', 'vk6.65424', 'vk6.65758'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is c. |
| The reverse -K is |
| The mirror image K* is |
| The reversed mirror image -K* is |
| The fillings (up to the first 10) associated to the algebraic genus: |
| Or click here to check the fillings |
| invariant | value |
|---|---|
| Gauss code | O1O2O3O4O5U3U4O6U1U6U5U2 |
| R3 orbit | {'O1O2O3O4U2O5U4O6U1U6U3U5', 'O1O2O3O4O5U3U4O6U1U6U5U2'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U4U1U6U5O6U2U3 |
| Gauss code of K* | O1O2O3O4U1U4U5U6U3O5O6U2 |
| Gauss code of -K* | O1O2O3O4U3O5O6U2U5U6U1U4 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 1 -2 0 3 1],[ 3 0 3 -1 1 4 1],[-1 -3 0 -2 0 2 0],[ 2 1 2 0 1 2 0],[ 0 -1 0 -1 0 1 0],[-3 -4 -2 -2 -1 0 0],[-1 -1 0 0 0 0 0]] |
| Primitive based matrix | [[ 0 3 1 1 0 -2 -3],[-3 0 0 -2 -1 -2 -4],[-1 0 0 0 0 0 -1],[-1 2 0 0 0 -2 -3],[ 0 1 0 0 0 -1 -1],[ 2 2 0 2 1 0 1],[ 3 4 1 3 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,-1,0,2,3,0,2,1,2,4,0,0,0,1,0,2,3,1,1,-1] |
| Phi over symmetry | [-3,-2,0,1,1,3,-1,1,1,3,4,1,0,2,2,0,0,1,0,0,2] |
| Phi of -K | [-3,-2,0,1,1,3,2,2,1,3,2,1,1,3,3,1,1,2,0,0,2] |
| Phi of K* | [-3,-1,-1,0,2,3,0,2,2,3,2,0,1,1,1,1,3,3,1,2,2] |
| Phi of -K* | [-3,-2,0,1,1,3,-1,1,1,3,4,1,0,2,2,0,0,1,0,0,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z+7 |
| Enhanced Jones-Krushkal polynomial | -10w^3z+13w^2z+7w |
| Inner characteristic polynomial | t^6+42t^4+17t^2 |
| Outer characteristic polynomial | t^7+66t^5+46t^3 |
| Flat arrow polynomial | 8*K1**3 - 2*K1**2 - 8*K1*K2 - 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -448*K1**2*K2**4 + 352*K1**2*K2**3 - 1984*K1**2*K2**2 + 1096*K1**2*K2 - 16*K1**2*K3**2 - 972*K1**2 + 672*K1*K2**3*K3 + 2008*K1*K2*K3 + 224*K1*K3*K4 + 56*K1*K4*K5 - 192*K2**6 + 288*K2**4*K4 - 920*K2**4 - 368*K2**2*K3**2 - 160*K2**2*K4**2 + 664*K2**2*K4 - 432*K2**2 + 96*K2*K3*K5 + 56*K2*K4*K6 - 16*K3**4 + 32*K3**2*K6 - 692*K3**2 - 330*K4**2 - 40*K5**2 - 24*K6**2 + 1048 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |