| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,0,1,2,1,0,0,1,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1442'] |
| 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+26t^5+61t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1442'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 576*K1**4*K2 - 3344*K1**4 + 288*K1**3*K2*K3 - 992*K1**3*K3 - 2464*K1**2*K2**2 - 128*K1**2*K2*K4 + 7600*K1**2*K2 - 464*K1**2*K3**2 - 4364*K1**2 + 4336*K1*K2*K3 + 408*K1*K3*K4 - 136*K2**4 + 136*K2**2*K4 - 3384*K2**2 - 1388*K3**2 - 126*K4**2 + 3508 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1442'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20015', 'vk6.20062', 'vk6.21285', 'vk6.21344', 'vk6.27066', 'vk6.27123', 'vk6.28769', 'vk6.28812', 'vk6.38463', 'vk6.38528', 'vk6.40650', 'vk6.40725', 'vk6.45347', 'vk6.45424', 'vk6.47114', 'vk6.47166', 'vk6.56830', 'vk6.56883', 'vk6.57962', 'vk6.58021', 'vk6.61348', 'vk6.61409', 'vk6.62522', 'vk6.62566', 'vk6.66550', 'vk6.66591', 'vk6.67337', 'vk6.67382', 'vk6.69196', 'vk6.69239', 'vk6.69945', 'vk6.69980'] |
| 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 | O1O2O3U4O5U2O4U1U3O6U5U6 |
| R3 orbit | {'O1O2O3U4O5U2O4U1U3O6U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O4U1U3O6U2O5U6 |
| Gauss code of K* | O1O2U3O4O3U1U5U2O6U4O5U6 |
| Gauss code of -K* | O1O2U1O3O4U5O6U2O5U3U6U4 |
| 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 1 0 1 1],[ 2 0 1 2 1 2 1],[ 1 -1 0 0 1 1 1],[-1 -2 0 0 -1 0 1],[ 0 -1 -1 1 0 1 0],[-1 -2 -1 0 -1 0 1],[-1 -1 -1 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 -1 0 -2],[-1 -1 0 -1 0 -1 -1],[-1 0 1 0 -1 -1 -2],[ 0 1 0 1 0 -1 -1],[ 1 0 1 1 1 0 -1],[ 2 2 1 2 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,1,0,2,1,0,1,1,1,1,2,1,1,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,0,1,2,1,0,0,1,0,-1,-1] |
| Phi of -K | [-2,-1,0,1,1,1,0,1,1,1,2,0,1,2,1,0,0,1,0,-1,-1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,-1,1,1,2,0,0,1,1,0,2,1,0,1,0] |
| Phi of -K* | [-2,-1,0,1,1,1,1,1,1,2,2,1,1,0,1,0,1,1,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+18t^4+36t^2+4 |
| Outer characteristic polynomial | t^7+26t^5+61t^3+8t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 + 576*K1**4*K2 - 3344*K1**4 + 288*K1**3*K2*K3 - 992*K1**3*K3 - 2464*K1**2*K2**2 - 128*K1**2*K2*K4 + 7600*K1**2*K2 - 464*K1**2*K3**2 - 4364*K1**2 + 4336*K1*K2*K3 + 408*K1*K3*K4 - 136*K2**4 + 136*K2**2*K4 - 3384*K2**2 - 1388*K3**2 - 126*K4**2 + 3508 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {5}, {4}, {2, 3}], [{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {4}, {2, 3}, {1}], [{6}, {1, 5}, {4}, {2, 3}]] |
| If K is slice | False |