| Min(phi) over symmetries of the knot is: [-2,0,0,1,1,1,1,1,1,0,0,1,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['5.85', '6.1529', '7.14921', '7.31459', '7.38203', '7.42966', '7.44678'] |
| 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^6+13t^4+8t^2+1 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1529', '7.44678'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 2432*K1**4*K2 - 6368*K1**4 + 224*K1**3*K2*K3 - 1024*K1**3*K3 + 128*K1**2*K2**3 - 4880*K1**2*K2**2 - 96*K1**2*K2*K4 + 10592*K1**2*K2 - 96*K1**2*K3**2 - 3804*K1**2 - 64*K1*K2**2*K3 + 3792*K1*K2*K3 + 72*K1*K3*K4 - 104*K2**4 + 104*K2**2*K4 - 3584*K2**2 - 716*K3**2 - 30*K4**2 + 3612 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1529'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17110', 'vk6.17352', 'vk6.20573', 'vk6.21982', 'vk6.23505', 'vk6.23842', 'vk6.28035', 'vk6.29494', 'vk6.35654', 'vk6.36090', 'vk6.39441', 'vk6.41642', 'vk6.43017', 'vk6.43328', 'vk6.46025', 'vk6.47693', 'vk6.55249', 'vk6.55500', 'vk6.57455', 'vk6.58622', 'vk6.59655', 'vk6.60001', 'vk6.62126', 'vk6.63092', 'vk6.65055', 'vk6.65249', 'vk6.66983', 'vk6.67848', 'vk6.68319', 'vk6.68468', 'vk6.69598', 'vk6.70291'] |
| 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 | O1O2O3U2O4U5U1O6O5U3U6U4 |
| R3 orbit | {'O1O2O3U2O4U5U1O6O5U3U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U1O6O5U3U6O4U2 |
| Gauss code of K* | O1O2O3U4U5U1O5U3O6O4U2U6 |
| Gauss code of -K* | O1O2O3U4U2O5O4U1O6U3U6U5 |
| 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 0 2 0 0],[ 1 0 0 1 1 1 0],[ 1 0 0 1 1 1 1],[ 0 -1 -1 0 2 0 0],[-2 -1 -1 -2 0 -1 -1],[ 0 -1 -1 0 1 0 0],[ 0 0 -1 0 1 0 0]] |
| Primitive based matrix | [[ 0 2 0 0 -1 -1],[-2 0 -1 -1 -1 -1],[ 0 1 0 0 0 -1],[ 0 1 0 0 -1 -1],[ 1 1 0 1 0 0],[ 1 1 1 1 0 0]] |
| If based matrix primitive | False |
| Phi of primitive based matrix | [-2,0,0,1,1,1,1,1,1,0,0,1,1,1,0] |
| Phi over symmetry | [-2,0,0,1,1,1,1,1,1,0,0,1,1,1,0] |
| Phi of -K | [-1,-1,0,0,2,0,0,0,2,0,1,2,0,1,1] |
| Phi of K* | [-2,0,0,1,1,1,1,2,2,0,0,0,0,1,0] |
| Phi of -K* | [-1,-1,0,0,2,0,0,1,1,1,1,1,0,1,1] |
| 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^5+7t^3+3t |
| Outer characteristic polynomial | t^6+13t^4+8t^2+1 |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 2432*K1**4*K2 - 6368*K1**4 + 224*K1**3*K2*K3 - 1024*K1**3*K3 + 128*K1**2*K2**3 - 4880*K1**2*K2**2 - 96*K1**2*K2*K4 + 10592*K1**2*K2 - 96*K1**2*K3**2 - 3804*K1**2 - 64*K1*K2**2*K3 + 3792*K1*K2*K3 + 72*K1*K3*K4 - 104*K2**4 + 104*K2**2*K4 - 3584*K2**2 - 716*K3**2 - 30*K4**2 + 3612 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {4, 5}, {3}, {1, 2}]] |
| If K is slice | False |