| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,1,1,2,2,-1,0,0,0,0,0,1,1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1649'] |
| 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+21t^5+31t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1649'] |
| 2-strand cable arrow polynomial of the knot is: 576*K1**4*K2 - 3168*K1**4 - 288*K1**3*K3 + 512*K1**2*K2**3 - 5488*K1**2*K2**2 - 96*K1**2*K2*K4 + 10512*K1**2*K2 - 128*K1**2*K3**2 - 6660*K1**2 - 768*K1*K2**2*K3 + 6528*K1*K2*K3 + 368*K1*K3*K4 - 840*K2**4 + 920*K2**2*K4 - 4928*K2**2 - 1900*K3**2 - 250*K4**2 + 5096 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1649'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.72418', 'vk6.72426', 'vk6.72469', 'vk6.72475', 'vk6.72476', 'vk6.72486', 'vk6.72828', 'vk6.72837', 'vk6.72838', 'vk6.72851', 'vk6.72891', 'vk6.72900', 'vk6.74457', 'vk6.74462', 'vk6.74471', 'vk6.74474', 'vk6.75072', 'vk6.75075', 'vk6.76968', 'vk6.77778', 'vk6.77784', 'vk6.77969', 'vk6.79461', 'vk6.79464', 'vk6.79910', 'vk6.79915', 'vk6.79921', 'vk6.79930', 'vk6.80933', 'vk6.80935', 'vk6.87229', 'vk6.89360'] |
| 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 | O1O2O3U1O4U3U5U2O6O5U4U6 |
| R3 orbit | {'O1O2O3U1O4U3U5U2O6O5U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O6O4U2U6U1O5U3 |
| Gauss code of K* | O1O2O3U4U2O5O4U6U3U1O6U5 |
| Gauss code of -K* | O1O2O3U4O5U3U1U5O6O4U2U6 |
| 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 0 1 0 0],[ 2 0 2 1 2 1 0],[-1 -2 0 0 1 -1 0],[ 0 -1 0 0 1 0 1],[-1 -2 -1 -1 0 -1 0],[ 0 -1 1 0 1 0 0],[ 0 0 0 -1 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 0 -2],[-1 0 1 0 0 -1 -2],[-1 -1 0 0 -1 -1 -2],[ 0 0 0 0 -1 0 0],[ 0 0 1 1 0 0 -1],[ 0 1 1 0 0 0 -1],[ 2 2 2 0 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,0,2,-1,0,0,1,2,0,1,1,2,1,0,0,0,1,1] |
| Phi over symmetry | [-2,0,0,0,1,1,0,1,1,2,2,-1,0,0,0,0,0,1,1,1,1] |
| Phi of -K | [-2,0,0,0,1,1,1,1,2,1,1,0,-1,0,1,0,0,0,1,1,1] |
| Phi of K* | [-1,-1,0,0,0,2,-1,0,0,1,1,0,1,1,1,0,0,1,1,1,2] |
| Phi of -K* | [-2,0,0,0,1,1,0,1,1,2,2,-1,0,0,0,0,0,1,1,1,1] |
| 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+15t^4+16t^2+1 |
| Outer characteristic polynomial | t^7+21t^5+31t^3+8t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | 576*K1**4*K2 - 3168*K1**4 - 288*K1**3*K3 + 512*K1**2*K2**3 - 5488*K1**2*K2**2 - 96*K1**2*K2*K4 + 10512*K1**2*K2 - 128*K1**2*K3**2 - 6660*K1**2 - 768*K1*K2**2*K3 + 6528*K1*K2*K3 + 368*K1*K3*K4 - 840*K2**4 + 920*K2**2*K4 - 4928*K2**2 - 1900*K3**2 - 250*K4**2 + 5096 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |