| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,1,1,2,4,0,0,1,1,1,0,2,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1064'] |
| Arrow polynomial of the knot is: -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.323', '6.380', '6.444', '6.472', '6.523', '6.579', '6.592', '6.595', '6.609', '6.614', '6.620', '6.644', '6.648', '6.669', '6.671', '6.681', '6.693', '6.724', '6.725', '6.757', '6.766', '6.785', '6.786', '6.797', '6.798', '6.816', '6.833', '6.972', '6.978', '6.1056', '6.1064', '6.1066', '6.1087', '6.1094', '6.1273', '6.1277', '6.1282', '6.1295', '6.1300', '6.1313', '6.1344', '6.1353', '6.1354'] |
| Outer characteristic polynomial of the knot is: t^7+46t^5+92t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1064'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 64*K1**4*K2 - 336*K1**4 + 192*K1**3*K2*K3 - 352*K1**3*K3 + 1536*K1**2*K2**3 - 5104*K1**2*K2**2 - 256*K1**2*K2*K4 + 5912*K1**2*K2 - 336*K1**2*K3**2 - 96*K1**2*K3*K5 - 4880*K1**2 + 224*K1*K2**3*K3 - 1216*K1*K2**2*K3 - 256*K1*K2*K3*K4 + 6072*K1*K2*K3 + 712*K1*K3*K4 + 152*K1*K4*K5 + 24*K1*K5*K6 - 1864*K2**4 - 368*K2**2*K3**2 - 8*K2**2*K4**2 + 1616*K2**2*K4 - 2894*K2**2 + 456*K2*K3*K5 + 16*K2*K4*K6 - 1916*K3**2 - 454*K4**2 - 164*K5**2 - 18*K6**2 + 3604 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1064'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73752', 'vk6.73761', 'vk6.73892', 'vk6.73899', 'vk6.75695', 'vk6.75706', 'vk6.75892', 'vk6.75898', 'vk6.78681', 'vk6.78697', 'vk6.78881', 'vk6.78894', 'vk6.80304', 'vk6.80318', 'vk6.80432', 'vk6.80441', 'vk6.81696', 'vk6.81704', 'vk6.81709', 'vk6.81799', 'vk6.82201', 'vk6.82452', 'vk6.82464', 'vk6.82467', 'vk6.82469', 'vk6.84429', 'vk6.84440', 'vk6.84442', 'vk6.87781', 'vk6.88118', 'vk6.88395', 'vk6.89635'] |
| 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 | O1O2O3O4U5U2O6U3O5U1U6U4 |
| R3 orbit | {'O1O2O3O4U5U2O6U3O5U1U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U4O6U2O5U3U6 |
| Gauss code of K* | O1O2O3U1U4U5U3O6O4U2O5U6 |
| Gauss code of -K* | O1O2O3U4O5U2O6O4U1U5U6U3 |
| 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 3 -1 1],[ 2 0 0 2 4 0 1],[ 1 0 0 1 1 0 0],[ 0 -2 -1 0 1 0 0],[-3 -4 -1 -1 0 -2 -1],[ 1 0 0 0 2 0 1],[-1 -1 0 0 1 -1 0]] |
| Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 -1 -1 -1 -2 -4],[-1 1 0 0 0 -1 -1],[ 0 1 0 0 -1 0 -2],[ 1 1 0 1 0 0 0],[ 1 2 1 0 0 0 0],[ 2 4 1 2 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,1,1,2,1,1,1,2,4,0,0,1,1,1,0,2,0,0,0] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,1,1,2,4,0,0,1,1,1,0,2,0,0,0] |
| Phi of -K | [-2,-1,-1,0,1,3,1,1,0,2,1,0,0,2,3,1,1,2,1,2,1] |
| Phi of K* | [-3,-1,0,1,1,2,1,2,2,3,1,1,1,2,2,1,0,0,0,1,1] |
| Phi of -K* | [-2,-1,-1,0,1,3,0,0,2,1,4,0,0,1,2,1,0,1,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 5z^2+22z+25 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+7w^3z^2-2w^3z+24w^2z+25w |
| Inner characteristic polynomial | t^6+30t^4+39t^2 |
| Outer characteristic polynomial | t^7+46t^5+92t^3+8t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 64*K1**4*K2 - 336*K1**4 + 192*K1**3*K2*K3 - 352*K1**3*K3 + 1536*K1**2*K2**3 - 5104*K1**2*K2**2 - 256*K1**2*K2*K4 + 5912*K1**2*K2 - 336*K1**2*K3**2 - 96*K1**2*K3*K5 - 4880*K1**2 + 224*K1*K2**3*K3 - 1216*K1*K2**2*K3 - 256*K1*K2*K3*K4 + 6072*K1*K2*K3 + 712*K1*K3*K4 + 152*K1*K4*K5 + 24*K1*K5*K6 - 1864*K2**4 - 368*K2**2*K3**2 - 8*K2**2*K4**2 + 1616*K2**2*K4 - 2894*K2**2 + 456*K2*K3*K5 + 16*K2*K4*K6 - 1916*K3**2 - 454*K4**2 - 164*K5**2 - 18*K6**2 + 3604 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |