| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,1,2,0,1,-1,-1,1,0,-1,1,0,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1884'] |
| 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+17t^5+50t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1884'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**6 + 1600*K1**4*K2 - 5696*K1**4 + 288*K1**3*K2*K3 - 1952*K1**3*K3 - 3888*K1**2*K2**2 - 288*K1**2*K2*K4 + 12176*K1**2*K2 - 960*K1**2*K3**2 - 7372*K1**2 - 416*K1*K2**2*K3 + 8240*K1*K2*K3 + 1496*K1*K3*K4 - 72*K2**4 + 440*K2**2*K4 - 6000*K2**2 - 2972*K3**2 - 570*K4**2 + 6200 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1884'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3639', 'vk6.3736', 'vk6.3929', 'vk6.4026', 'vk6.4479', 'vk6.4576', 'vk6.5865', 'vk6.5994', 'vk6.7132', 'vk6.7309', 'vk6.7402', 'vk6.7918', 'vk6.8039', 'vk6.9352', 'vk6.17916', 'vk6.18013', 'vk6.18760', 'vk6.24455', 'vk6.24883', 'vk6.25346', 'vk6.37499', 'vk6.43890', 'vk6.44230', 'vk6.44535', 'vk6.48279', 'vk6.48344', 'vk6.50070', 'vk6.50184', 'vk6.50563', 'vk6.50628', 'vk6.55877', 'vk6.60738'] |
| 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 | O1O2O3U1U3O4U2O5U4O6U5U6 |
| R3 orbit | {'O1O2O3U1U3O4U2O5U4O6U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O4U6O5U2O6U1U3 |
| Gauss code of K* | O1O2U3O4U5O3U6O5O6U1U4U2 |
| Gauss code of -K* | O1O2U1O3U2O4U3O5O6U5U4U6 |
| 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 0 1 0 0 1],[ 2 0 2 1 1 0 0],[ 0 -2 0 0 1 1 0],[-1 -1 0 0 0 0 0],[ 0 -1 -1 0 0 1 1],[ 0 0 -1 0 -1 0 1],[-1 0 0 0 -1 -1 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 0 -2],[-1 0 0 0 0 0 -1],[-1 0 0 0 -1 -1 0],[ 0 0 0 0 1 1 -2],[ 0 0 1 -1 0 1 -1],[ 0 0 1 -1 -1 0 0],[ 2 1 0 2 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,0,2,0,0,0,0,1,0,1,1,0,-1,-1,2,-1,1,0] |
| Phi over symmetry | [-2,0,0,0,1,1,0,1,2,0,1,-1,-1,1,0,-1,1,0,0,0,0] |
| Phi of -K | [-2,0,0,0,1,1,0,1,2,2,3,-1,-1,1,1,-1,1,0,1,0,0] |
| Phi of K* | [-1,-1,0,0,0,2,0,0,0,1,3,1,1,1,2,-1,-1,2,-1,1,0] |
| Phi of -K* | [-2,0,0,0,1,1,0,1,2,0,1,-1,-1,1,0,-1,1,0,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 21z+43 |
| Enhanced Jones-Krushkal polynomial | 21w^2z+43w |
| Inner characteristic polynomial | t^6+11t^4+15t^2 |
| Outer characteristic polynomial | t^7+17t^5+50t^3+4t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -256*K1**6 + 1600*K1**4*K2 - 5696*K1**4 + 288*K1**3*K2*K3 - 1952*K1**3*K3 - 3888*K1**2*K2**2 - 288*K1**2*K2*K4 + 12176*K1**2*K2 - 960*K1**2*K3**2 - 7372*K1**2 - 416*K1*K2**2*K3 + 8240*K1*K2*K3 + 1496*K1*K3*K4 - 72*K2**4 + 440*K2**2*K4 - 6000*K2**2 - 2972*K3**2 - 570*K4**2 + 6200 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{2, 6}, {3, 5}, {1, 4}], [{3, 6}, {1, 5}, {2, 4}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{5, 6}, {2, 4}, {1, 3}], [{6}, {3, 5}, {4}, {1, 2}]] |
| If K is slice | False |