| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,2,1,1,2,1,1,1,2,1,1,0,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.947'] |
| 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+28t^5+35t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.947', '7.44581'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 544*K1**4*K2 - 2320*K1**4 + 96*K1**3*K2*K3 - 192*K1**3*K3 + 608*K1**2*K2**3 - 3728*K1**2*K2**2 - 128*K1**2*K2*K4 + 4864*K1**2*K2 - 48*K1**2*K3**2 - 1596*K1**2 - 544*K1*K2**2*K3 + 2928*K1*K2*K3 + 160*K1*K3*K4 - 792*K2**4 + 728*K2**2*K4 - 1488*K2**2 - 580*K3**2 - 150*K4**2 + 1700 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.947'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16547', 'vk6.16638', 'vk6.17518', 'vk6.17573', 'vk6.18872', 'vk6.18948', 'vk6.19201', 'vk6.19496', 'vk6.23068', 'vk6.23477', 'vk6.23814', 'vk6.24115', 'vk6.25502', 'vk6.25575', 'vk6.26007', 'vk6.26393', 'vk6.35065', 'vk6.35618', 'vk6.36305', 'vk6.36374', 'vk6.37599', 'vk6.37686', 'vk6.38887', 'vk6.41089', 'vk6.42517', 'vk6.42626', 'vk6.43482', 'vk6.44588', 'vk6.45648', 'vk6.54777', 'vk6.54867', 'vk6.56437', 'vk6.58229', 'vk6.59295', 'vk6.59973', 'vk6.60175', 'vk6.62788', 'vk6.65027', 'vk6.66096', 'vk6.66136'] |
| 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 | O1O2O3O4U5U1O6O5U3U4U6U2 |
| R3 orbit | {'O1O2O3O4U5U1O6O5U3U4U6U2', 'O1O2O3U4O5U1O4O6U3U6U5U2'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U3U5U1U2O6O5U4U6 |
| Gauss code of K* | O1O2O3O4U5U4U1U2O6O5U3U6 |
| Gauss code of -K* | O1O2O3O4U5U2O6O5U3U4U1U6 |
| 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 1 0 1],[ 2 0 2 0 1 2 1],[-1 -2 0 -2 0 0 1],[ 1 0 2 0 1 1 1],[-1 -1 0 -1 0 -1 0],[ 0 -2 0 -1 1 0 1],[-1 -1 -1 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 0 -2 -2],[-1 -1 0 0 -1 -1 -1],[-1 0 0 0 -1 -1 -1],[ 0 0 1 1 0 -1 -2],[ 1 2 1 1 1 0 0],[ 2 2 1 1 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,0,2,2,0,1,1,1,1,1,1,1,2,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,2,1,1,2,1,1,1,2,1,1,0,0,-1,0] |
| Phi of -K | [-2,-1,0,1,1,1,1,0,1,2,2,0,0,1,1,1,0,0,-1,0,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,0,1,2,0,1,0,1,0,1,2,0,0,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,2,1,1,2,1,1,1,2,1,1,0,0,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 2z^2+15z+23 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+15w^2z+23w |
| Inner characteristic polynomial | t^6+20t^4+18t^2+1 |
| Outer characteristic polynomial | t^7+28t^5+35t^3+4t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 544*K1**4*K2 - 2320*K1**4 + 96*K1**3*K2*K3 - 192*K1**3*K3 + 608*K1**2*K2**3 - 3728*K1**2*K2**2 - 128*K1**2*K2*K4 + 4864*K1**2*K2 - 48*K1**2*K3**2 - 1596*K1**2 - 544*K1*K2**2*K3 + 2928*K1*K2*K3 + 160*K1*K3*K4 - 792*K2**4 + 728*K2**2*K4 - 1488*K2**2 - 580*K3**2 - 150*K4**2 + 1700 |
| Genus of based matrix | 2 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{1, 6}, {5}, {2, 4}, {3}], [{1, 6}, {5}, {3, 4}, {2}], [{1, 6}, {5}, {4}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{2, 6}, {5}, {1, 4}, {3}], [{2, 6}, {5}, {3, 4}, {1}], [{2, 6}, {5}, {4}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}], [{3, 6}, {5}, {1, 4}, {2}], [{3, 6}, {5}, {2, 4}, {1}], [{3, 6}, {5}, {4}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{4, 6}, {5}, {1, 3}, {2}], [{4, 6}, {5}, {2, 3}, {1}], [{4, 6}, {5}, {3}, {1, 2}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}], [{5, 6}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}], [{5, 6}, {4}, {1, 3}, {2}], [{5, 6}, {4}, {2, 3}, {1}], [{5, 6}, {4}, {3}, {1, 2}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {3, 5}, {1, 4}, {2}], [{6}, {3, 5}, {2, 4}, {1}], [{6}, {3, 5}, {4}, {1, 2}], [{6}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {4, 5}, {3}, {2}, {1}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {1, 3}, {2}], [{6}, {5}, {4}, {2, 3}, {1}], [{6}, {5}, {4}, {3}, {1, 2}]] |
| If K is slice | False |