| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,1,1,1,0,2,-1,-1,1,1,0,0,0,1,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1960'] |
| 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+25t^5+63t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1960'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**6 - 832*K1**4*K2**2 + 1664*K1**4*K2 - 5232*K1**4 + 704*K1**3*K2*K3 - 832*K1**3*K3 + 864*K1**2*K2**3 - 7712*K1**2*K2**2 - 416*K1**2*K2*K4 + 11120*K1**2*K2 - 112*K1**2*K3**2 - 3936*K1**2 - 480*K1*K2**2*K3 + 6560*K1*K2*K3 + 240*K1*K3*K4 - 552*K2**4 + 544*K2**2*K4 - 3672*K2**2 - 1344*K3**2 - 146*K4**2 + 3824 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1960'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4688', 'vk6.4991', 'vk6.6170', 'vk6.6641', 'vk6.8167', 'vk6.8585', 'vk6.9557', 'vk6.9896', 'vk6.17392', 'vk6.20912', 'vk6.20983', 'vk6.22322', 'vk6.22407', 'vk6.23559', 'vk6.23896', 'vk6.28388', 'vk6.36160', 'vk6.40042', 'vk6.40184', 'vk6.42093', 'vk6.43071', 'vk6.43375', 'vk6.46570', 'vk6.46689', 'vk6.48728', 'vk6.49520', 'vk6.49723', 'vk6.51428', 'vk6.55558', 'vk6.58910', 'vk6.65296', 'vk6.69764'] |
| 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 | O1O2U1O3O4U5U6O5U2O6U3U4 |
| R3 orbit | {'O1O2U1O3O4U5U6O5U2O6U3U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2U3O4O3U1U2O5U4O6U5U6 |
| Gauss code of K* | O1O2U1O3U2O4O5U6U3O6U4U5 |
| Gauss code of -K* | O1O2U3O4U5O3O5U1U2O6U4U6 |
| 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 0 0 2 -1 0],[ 1 0 1 1 1 1 0],[ 0 -1 0 0 1 0 1],[ 0 -1 0 0 1 -1 1],[-2 -1 -1 -1 0 -3 -1],[ 1 -1 0 1 3 0 0],[ 0 0 -1 -1 1 0 0]] |
| Primitive based matrix | [[ 0 2 0 0 0 -1 -1],[-2 0 -1 -1 -1 -1 -3],[ 0 1 0 1 0 -1 0],[ 0 1 -1 0 -1 0 0],[ 0 1 0 1 0 -1 -1],[ 1 1 1 0 1 0 1],[ 1 3 0 0 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,0,0,0,1,1,1,1,1,1,3,-1,0,1,0,1,0,0,1,1,-1] |
| Phi over symmetry | [-2,0,0,0,1,1,1,1,1,0,2,-1,-1,1,1,0,0,0,1,0,-1] |
| Phi of -K | [-1,-1,0,0,0,2,-1,0,0,1,2,0,1,1,0,0,-1,1,-1,1,1] |
| Phi of K* | [-2,0,0,0,1,1,1,1,1,0,2,-1,-1,1,1,0,0,0,1,0,-1] |
| Phi of -K* | [-1,-1,0,0,0,2,-1,0,0,1,3,0,1,1,1,-1,-1,1,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 5z^2+26z+33 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+26w^2z+33w |
| Inner characteristic polynomial | t^6+19t^4+44t^2+4 |
| Outer characteristic polynomial | t^7+25t^5+63t^3+11t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -256*K1**6 - 832*K1**4*K2**2 + 1664*K1**4*K2 - 5232*K1**4 + 704*K1**3*K2*K3 - 832*K1**3*K3 + 864*K1**2*K2**3 - 7712*K1**2*K2**2 - 416*K1**2*K2*K4 + 11120*K1**2*K2 - 112*K1**2*K3**2 - 3936*K1**2 - 480*K1*K2**2*K3 + 6560*K1*K2*K3 + 240*K1*K3*K4 - 552*K2**4 + 544*K2**2*K4 - 3672*K2**2 - 1344*K3**2 - 146*K4**2 + 3824 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}]] |
| If K is slice | False |