| Min(phi) over symmetries of the knot is: [-1,-1,0,0,1,1,0,0,0,1,1,0,1,1,2,-1,0,0,1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1816', '6.2014', '7.44900'] |
| Arrow polynomial of the knot is: -12*K1**2 + 6*K2 + 7 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.612', '6.1246', '6.1402', '6.1410', '6.1411', '6.1468', '6.1617', '6.1666', '6.1667', '6.1815', '6.1904', '6.1994', '6.1995', '6.1996', '6.2001', '6.2014', '6.2015', '6.2016', '6.2017', '6.2020', '6.2022'] |
| Outer characteristic polynomial of the knot is: t^7+14t^5+25t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1816', '6.2014', '7.44900'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**6 - 320*K1**4*K2**2 + 3808*K1**4*K2 - 6864*K1**4 + 256*K1**3*K2*K3 - 1216*K1**3*K3 + 2112*K1**2*K2**3 - 10432*K1**2*K2**2 - 448*K1**2*K2*K4 + 12904*K1**2*K2 - 112*K1**2*K3**2 - 4148*K1**2 - 1888*K1*K2**2*K3 + 7768*K1*K2*K3 + 480*K1*K3*K4 - 1600*K2**4 + 1616*K2**2*K4 - 4072*K2**2 - 1452*K3**2 - 312*K4**2 + 4366 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2014'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11265', 'vk6.11345', 'vk6.12526', 'vk6.12639', 'vk6.17614', 'vk6.18920', 'vk6.18996', 'vk6.19349', 'vk6.19642', 'vk6.24068', 'vk6.24162', 'vk6.25516', 'vk6.25615', 'vk6.26125', 'vk6.26543', 'vk6.30939', 'vk6.31064', 'vk6.32115', 'vk6.32236', 'vk6.36417', 'vk6.37661', 'vk6.37708', 'vk6.43516', 'vk6.44786', 'vk6.52031', 'vk6.52120', 'vk6.52941', 'vk6.56499', 'vk6.56647', 'vk6.65385', 'vk6.66129', 'vk6.66163'] |
| 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 | O1O2U3O4U1O5U4U6O3O6U5U2 |
| R3 orbit | {'O1O2U3O4U1O5U4U6O3O6U5U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2U1U3O4O5U4U6O3U2O6U5 |
| Gauss code of K* | O1O2U3U2O4O5U6U5O3U1O6U4 |
| Gauss code of -K* | O1O2U3O4U2O5U6U4O6O3U1U5 |
| 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 -1 0 0 1],[ 1 0 1 0 1 0 2],[-1 -1 0 -1 -1 0 0],[ 1 0 1 0 0 0 1],[ 0 -1 1 0 0 1 0],[ 0 0 0 0 -1 0 0],[-1 -2 0 -1 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 -1 -1],[-1 0 0 0 0 -1 -2],[-1 0 0 0 -1 -1 -1],[ 0 0 0 0 -1 0 0],[ 0 0 1 1 0 0 -1],[ 1 1 1 0 0 0 0],[ 1 2 1 0 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,1,1,0,0,0,1,2,0,1,1,1,1,0,0,0,1,0] |
| Phi over symmetry | [-1,-1,0,0,1,1,0,0,0,1,1,0,1,1,2,-1,0,0,1,0,0] |
| Phi of -K | [-1,-1,0,0,1,1,0,0,1,0,1,1,1,1,1,-1,1,0,1,1,0] |
| Phi of K* | [-1,-1,0,0,1,1,0,0,1,1,1,1,1,0,1,1,0,1,1,1,0] |
| Phi of -K* | [-1,-1,0,0,1,1,0,0,0,1,1,0,1,1,2,-1,0,0,1,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+10t^4+15t^2+1 |
| Outer characteristic polynomial | t^7+14t^5+25t^3+4t |
| Flat arrow polynomial | -12*K1**2 + 6*K2 + 7 |
| 2-strand cable arrow polynomial | -448*K1**6 - 320*K1**4*K2**2 + 3808*K1**4*K2 - 6864*K1**4 + 256*K1**3*K2*K3 - 1216*K1**3*K3 + 2112*K1**2*K2**3 - 10432*K1**2*K2**2 - 448*K1**2*K2*K4 + 12904*K1**2*K2 - 112*K1**2*K3**2 - 4148*K1**2 - 1888*K1*K2**2*K3 + 7768*K1*K2*K3 + 480*K1*K3*K4 - 1600*K2**4 + 1616*K2**2*K4 - 4072*K2**2 - 1452*K3**2 - 312*K4**2 + 4366 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {5}, {4}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |