| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,2,3,0,0,0,2,1,2,0,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1612'] |
| 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+34t^5+108t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1612'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 - 192*K1**4*K2**2 + 1376*K1**4*K2 - 6128*K1**4 + 352*K1**3*K2*K3 - 640*K1**3*K3 - 4800*K1**2*K2**2 - 96*K1**2*K2*K4 + 11272*K1**2*K2 - 176*K1**2*K3**2 - 4684*K1**2 - 320*K1*K2**2*K3 + 5240*K1*K2*K3 + 312*K1*K3*K4 - 168*K2**4 + 328*K2**2*K4 - 4496*K2**2 - 1452*K3**2 - 162*K4**2 + 4496 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1612'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4239', 'vk6.4259', 'vk6.4319', 'vk6.4338', 'vk6.5514', 'vk6.5536', 'vk6.5633', 'vk6.5655', 'vk6.7709', 'vk6.7728', 'vk6.9111', 'vk6.9128', 'vk6.9191', 'vk6.9207', 'vk6.19826', 'vk6.19837', 'vk6.26261', 'vk6.26274', 'vk6.26704', 'vk6.26719', 'vk6.38211', 'vk6.38224', 'vk6.44984', 'vk6.45001', 'vk6.48561', 'vk6.48569', 'vk6.49272', 'vk6.49278', 'vk6.50410', 'vk6.50417', 'vk6.66365', 'vk6.66368'] |
| 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 | O1O2O3U2O4U5U6O5U1O6U4U3 |
| R3 orbit | {'O1O2O3U2O4U5U6O5U1O6U4U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U4O5U3O6U5U6O4U2 |
| Gauss code of K* | O1O2U1O3U2O4O5U3U6U5O6U4 |
| Gauss code of -K* | O1O2U3O4U5O3O5U2O6U1U6U4 |
| 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 1 2],[ 1 0 0 1 0 1 1],[-2 -2 -1 0 0 -3 -1],[-1 0 0 0 0 -2 0],[ 1 -1 -1 3 2 0 0],[ 0 -2 -1 1 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 0 -1 -1 -2 -3],[-1 0 0 0 0 0 -2],[ 0 1 0 0 -1 -2 0],[ 1 1 0 1 0 0 1],[ 1 2 0 2 0 0 1],[ 1 3 2 0 -1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,0,1,1,2,3,0,0,0,2,1,2,0,0,-1,-1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,2,3,0,0,0,2,1,2,0,0,-1,-1] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,-1,2,1,1,1,0,0,0,2,2,1,1,1] |
| Phi of K* | [-2,-1,0,1,1,1,1,1,0,1,2,1,0,2,2,1,-1,0,-1,-1,0] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,-1,0,2,3,0,1,0,1,2,0,2,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 2z^2+23z+39 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+23w^2z+39w |
| Inner characteristic polynomial | t^6+26t^4+75t^2 |
| Outer characteristic polynomial | t^7+34t^5+108t^3+4t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 - 192*K1**4*K2**2 + 1376*K1**4*K2 - 6128*K1**4 + 352*K1**3*K2*K3 - 640*K1**3*K3 - 4800*K1**2*K2**2 - 96*K1**2*K2*K4 + 11272*K1**2*K2 - 176*K1**2*K3**2 - 4684*K1**2 - 320*K1*K2**2*K3 + 5240*K1*K2*K3 + 312*K1*K3*K4 - 168*K2**4 + 328*K2**2*K4 - 4496*K2**2 - 1452*K3**2 - 162*K4**2 + 4496 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {3, 5}, {1, 2}]] |
| If K is slice | False |