| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,1,1,1,1,0,1,-1,-1,-1,1,1,0,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1887'] |
| 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+31t^5+91t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1887'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 928*K1**4*K2 - 3040*K1**4 + 224*K1**3*K2*K3 - 256*K1**3*K3 + 480*K1**2*K2**3 - 6800*K1**2*K2**2 - 224*K1**2*K2*K4 + 10400*K1**2*K2 - 64*K1**2*K3**2 - 5852*K1**2 - 352*K1*K2**2*K3 + 5872*K1*K2*K3 + 176*K1*K3*K4 - 424*K2**4 + 424*K2**2*K4 - 4200*K2**2 - 1300*K3**2 - 110*K4**2 + 4308 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1887'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71388', 'vk6.71447', 'vk6.71910', 'vk6.71969', 'vk6.72452', 'vk6.72603', 'vk6.72722', 'vk6.72815', 'vk6.72878', 'vk6.73031', 'vk6.74234', 'vk6.74364', 'vk6.74437', 'vk6.74862', 'vk6.75052', 'vk6.76626', 'vk6.76914', 'vk6.77053', 'vk6.77417', 'vk6.77762', 'vk6.77812', 'vk6.79286', 'vk6.79402', 'vk6.79759', 'vk6.79818', 'vk6.79887', 'vk6.80852', 'vk6.80914', 'vk6.81377', 'vk6.85504', 'vk6.87223', 'vk6.89269'] |
| 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 | O1O2O3U1U4O5U6O4U2O6U3U5 |
| R3 orbit | {'O1O2O3U1U4O5U6O4U2O6U3U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1O5U2O6U5O4U6U3 |
| Gauss code of K* | O1O2U3O4U2O5U4O6O3U1U5U6 |
| Gauss code of -K* | O1O2U3O4U5O3U1O5O6U2U4U6 |
| 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 0 1 0 1 0],[ 2 0 1 2 2 2 1],[ 0 -1 0 0 0 0 1],[-1 -2 0 0 -2 0 0],[ 0 -2 0 2 0 2 -1],[-1 -2 0 0 -2 0 -1],[ 0 -1 -1 0 1 1 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 0 -2],[-1 0 0 0 0 -2 -2],[-1 0 0 0 -1 -2 -2],[ 0 0 0 0 1 0 -1],[ 0 0 1 -1 0 1 -1],[ 0 2 2 0 -1 0 -2],[ 2 2 2 1 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,0,2,0,0,0,2,2,0,1,2,2,-1,0,1,-1,1,2] |
| Phi over symmetry | [-2,0,0,0,1,1,0,1,1,1,1,0,1,-1,-1,-1,1,1,0,1,0] |
| Phi of -K | [-2,0,0,0,1,1,0,1,1,1,1,0,1,-1,-1,-1,1,1,0,1,0] |
| Phi of K* | [-1,-1,0,0,0,2,0,-1,0,1,1,-1,1,1,1,-1,0,0,-1,1,1] |
| Phi of -K* | [-2,0,0,0,1,1,1,1,2,2,2,-1,1,0,1,0,0,0,2,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+25t^4+66t^2+4 |
| Outer characteristic polynomial | t^7+31t^5+91t^3+11t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 928*K1**4*K2 - 3040*K1**4 + 224*K1**3*K2*K3 - 256*K1**3*K3 + 480*K1**2*K2**3 - 6800*K1**2*K2**2 - 224*K1**2*K2*K4 + 10400*K1**2*K2 - 64*K1**2*K3**2 - 5852*K1**2 - 352*K1*K2**2*K3 + 5872*K1*K2*K3 + 176*K1*K3*K4 - 424*K2**4 + 424*K2**2*K4 - 4200*K2**2 - 1300*K3**2 - 110*K4**2 + 4308 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |