| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,-1,1,1,2,2,1,0,0,1,0,0,0,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1616'] |
| 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+22t^5+29t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1616'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 - 64*K1**4*K2**2 + 1760*K1**4*K2 - 5392*K1**4 + 288*K1**3*K2*K3 - 896*K1**3*K3 + 96*K1**2*K2**3 - 4256*K1**2*K2**2 - 288*K1**2*K2*K4 + 8728*K1**2*K2 - 432*K1**2*K3**2 - 3036*K1**2 + 4008*K1*K2*K3 + 472*K1*K3*K4 - 168*K2**4 + 176*K2**2*K4 - 2992*K2**2 - 924*K3**2 - 146*K4**2 + 3128 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1616'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4081', 'vk6.4114', 'vk6.5319', 'vk6.5352', 'vk6.7449', 'vk6.7482', 'vk6.8950', 'vk6.8983', 'vk6.10119', 'vk6.10284', 'vk6.10309', 'vk6.14536', 'vk6.15268', 'vk6.15397', 'vk6.15760', 'vk6.16175', 'vk6.29859', 'vk6.29892', 'vk6.33906', 'vk6.33991', 'vk6.34203', 'vk6.34372', 'vk6.48465', 'vk6.49166', 'vk6.50217', 'vk6.50248', 'vk6.51611', 'vk6.53965', 'vk6.54030', 'vk6.54176', 'vk6.54466', 'vk6.63322'] |
| 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 | O1O2O3U2O4U5U4O6U1O5U6U3 |
| R3 orbit | {'O1O2O3U2O4U5U4O6U1O5U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U4O5U3O4U6U5O6U2 |
| Gauss code of K* | O1O2U3O4U1O3O5U4U6U5O6U2 |
| Gauss code of -K* | O1O2U3O4U2O5O3U5O6U1U6U4 |
| 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 -1 -1 2 1 -1 0],[ 1 0 0 2 0 0 0],[ 1 0 0 1 0 1 0],[-2 -2 -1 0 1 -2 -1],[-1 0 0 -1 0 -1 -1],[ 1 0 -1 2 1 0 0],[ 0 0 0 1 1 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 1 -1 -1 -2 -2],[-1 -1 0 -1 0 0 -1],[ 0 1 1 0 0 0 0],[ 1 1 0 0 0 0 1],[ 1 2 0 0 0 0 0],[ 1 2 1 0 -1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,-1,1,1,2,2,1,0,0,1,0,0,0,0,-1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,-1,1,1,2,2,1,0,0,1,0,0,0,0,-1,0] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,1,2,2,0,1,1,1,1,2,1,0,1,2] |
| Phi of K* | [-2,-1,0,1,1,1,2,1,1,1,2,0,1,2,2,1,1,1,0,-1,0] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,1,2,0,0,0,1,0,0,2,1,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 2z^2+21z+35 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+21w^2z+35w |
| Inner characteristic polynomial | t^6+14t^4+16t^2+4 |
| Outer characteristic polynomial | t^7+22t^5+29t^3+9t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 - 64*K1**4*K2**2 + 1760*K1**4*K2 - 5392*K1**4 + 288*K1**3*K2*K3 - 896*K1**3*K3 + 96*K1**2*K2**3 - 4256*K1**2*K2**2 - 288*K1**2*K2*K4 + 8728*K1**2*K2 - 432*K1**2*K3**2 - 3036*K1**2 + 4008*K1*K2*K3 + 472*K1*K3*K4 - 168*K2**4 + 176*K2**2*K4 - 2992*K2**2 - 924*K3**2 - 146*K4**2 + 3128 |
| Genus of based matrix | 2 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{1, 6}, {5}, {2, 4}, {3}], [{1, 6}, {5}, {3, 4}, {2}], [{1, 6}, {5}, {4}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{2, 6}, {5}, {1, 4}, {3}], [{2, 6}, {5}, {3, 4}, {1}], [{2, 6}, {5}, {4}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}], [{3, 6}, {5}, {1, 4}, {2}], [{3, 6}, {5}, {2, 4}, {1}], [{3, 6}, {5}, {4}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{4, 6}, {5}, {1, 3}, {2}], [{4, 6}, {5}, {2, 3}, {1}], [{4, 6}, {5}, {3}, {1, 2}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}], [{5, 6}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}], [{5, 6}, {4}, {1, 3}, {2}], [{5, 6}, {4}, {2, 3}, {1}], [{5, 6}, {4}, {3}, {1, 2}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {1, 5}, {4}, {3}, {2}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {3, 5}, {1, 4}, {2}], [{6}, {3, 5}, {2, 4}, {1}], [{6}, {3, 5}, {4}, {1, 2}], [{6}, {3, 5}, {4}, {2}, {1}], [{6}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {1, 3}, {2}]] |
| If K is slice | False |