| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-1,0,1,3,2,0,1,2,2,0,0,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1476'] |
| Arrow polynomial of the knot is: -10*K1**2 + 5*K2 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.947', '6.1027', '6.1399', '6.1430', '6.1433', '6.1442', '6.1465', '6.1469', '6.1476', '6.1505', '6.1529', '6.1606', '6.1612', '6.1613', '6.1616', '6.1649', '6.1694', '6.1736', '6.1768', '6.1771', '6.1774', '6.1884', '6.1886', '6.1887', '6.1889', '6.1960', '6.1962'] |
| Outer characteristic polynomial of the knot is: t^7+45t^5+101t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1476'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 1696*K1**4*K2 - 4608*K1**4 + 448*K1**3*K2*K3 - 832*K1**3*K3 + 96*K1**2*K2**3 - 5072*K1**2*K2**2 - 352*K1**2*K2*K4 + 10208*K1**2*K2 - 448*K1**2*K3**2 - 5488*K1**2 - 864*K1*K2**2*K3 + 6288*K1*K2*K3 + 888*K1*K3*K4 - 360*K2**4 + 792*K2**2*K4 - 4744*K2**2 - 1896*K3**2 - 402*K4**2 + 4712 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1476'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16936', 'vk6.17179', 'vk6.20552', 'vk6.21952', 'vk6.23332', 'vk6.23627', 'vk6.28007', 'vk6.29473', 'vk6.35372', 'vk6.35793', 'vk6.39421', 'vk6.41614', 'vk6.42845', 'vk6.43124', 'vk6.45997', 'vk6.47673', 'vk6.55099', 'vk6.55356', 'vk6.57419', 'vk6.58590', 'vk6.59497', 'vk6.59793', 'vk6.62086', 'vk6.63065', 'vk6.64944', 'vk6.65152', 'vk6.66962', 'vk6.67822', 'vk6.68233', 'vk6.68376', 'vk6.69574', 'vk6.70270'] |
| 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 | O1O2O3U4O5U2O4U1U6U3O6U5 |
| R3 orbit | {'O1O2O3U4O5U2O4U1U6U3O6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4O5U1U5U3O6U2O4U6 |
| Gauss code of K* | O1O2O3U2O4U1U5U3O6U4O5U6 |
| Gauss code of -K* | O1O2O3U4O5U6O4U1U5U3O6U2 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 3 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -1 2 0 2 -1],[ 2 0 1 2 1 2 1],[ 1 -1 0 0 1 1 0],[-2 -2 0 0 -2 -1 -2],[ 0 -1 -1 2 0 2 -1],[-2 -2 -1 1 -2 0 -2],[ 1 -1 0 2 1 2 0]] |
| Primitive based matrix | [[ 0 2 2 0 -1 -1 -2],[-2 0 1 -2 -1 -2 -2],[-2 -1 0 -2 0 -2 -2],[ 0 2 2 0 -1 -1 -1],[ 1 1 0 1 0 0 -1],[ 1 2 2 1 0 0 -1],[ 2 2 2 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,1,1,2,-1,2,1,2,2,2,0,2,2,1,1,1,0,1,1] |
| Phi over symmetry | [-2,-2,0,1,1,2,-1,0,1,3,2,0,1,2,2,0,0,1,0,0,0] |
| Phi of -K | [-2,-1,-1,0,2,2,0,0,1,2,2,0,0,1,1,0,2,3,0,0,-1] |
| Phi of K* | [-2,-2,0,1,1,2,-1,0,1,3,2,0,1,2,2,0,0,1,0,0,0] |
| Phi of -K* | [-2,-1,-1,0,2,2,1,1,1,2,2,0,1,0,1,1,2,2,2,2,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+31t^4+60t^2+4 |
| Outer characteristic polynomial | t^7+45t^5+101t^3+11t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 + 1696*K1**4*K2 - 4608*K1**4 + 448*K1**3*K2*K3 - 832*K1**3*K3 + 96*K1**2*K2**3 - 5072*K1**2*K2**2 - 352*K1**2*K2*K4 + 10208*K1**2*K2 - 448*K1**2*K3**2 - 5488*K1**2 - 864*K1*K2**2*K3 + 6288*K1*K2*K3 + 888*K1*K3*K4 - 360*K2**4 + 792*K2**2*K4 - 4744*K2**2 - 1896*K3**2 - 402*K4**2 + 4712 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |