| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,0,2,2,1,1,1,2,1,1,0,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1433'] |
| 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+45t^3+16t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1433'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**6 - 256*K1**4*K2**2 + 1568*K1**4*K2 - 4976*K1**4 + 640*K1**3*K2*K3 - 1472*K1**3*K3 - 4480*K1**2*K2**2 - 384*K1**2*K2*K4 + 10744*K1**2*K2 - 464*K1**2*K3**2 - 5460*K1**2 - 160*K1*K2**2*K3 + 6568*K1*K2*K3 + 512*K1*K3*K4 - 200*K2**4 + 296*K2**2*K4 - 4584*K2**2 - 1932*K3**2 - 166*K4**2 + 4652 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1433'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4122', 'vk6.4153', 'vk6.5360', 'vk6.5391', 'vk6.7490', 'vk6.7519', 'vk6.8991', 'vk6.9022', 'vk6.12438', 'vk6.12471', 'vk6.13356', 'vk6.13577', 'vk6.13608', 'vk6.14247', 'vk6.14694', 'vk6.14751', 'vk6.15194', 'vk6.15850', 'vk6.15905', 'vk6.30843', 'vk6.30876', 'vk6.32027', 'vk6.32060', 'vk6.33074', 'vk6.33105', 'vk6.33847', 'vk6.34307', 'vk6.48482', 'vk6.50267', 'vk6.53544', 'vk6.53930', 'vk6.54266'] |
| 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 | O1O2O3U2O4U3O5U6U4O6U1U5 |
| R3 orbit | {'O1O2O3U2O4U3O5U6U4O6U1U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U3O5U6U5O4U1O6U2 |
| Gauss code of K* | O1O2U1O3O4U3U5U6O5U2O6U4 |
| Gauss code of -K* | O1O2U3O4O3U1O5U4O6U5U6U2 |
| 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 0 1 2 -1],[ 1 0 -1 0 2 2 0],[ 1 1 0 1 1 0 1],[ 0 0 -1 0 1 1 -1],[-1 -2 -1 -1 0 0 -1],[-2 -2 0 -1 0 0 -2],[ 1 0 -1 1 1 2 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 0 -1 0 -2 -2],[-1 0 0 -1 -1 -1 -2],[ 0 1 1 0 -1 -1 0],[ 1 0 1 1 0 1 1],[ 1 2 1 1 -1 0 0],[ 1 2 2 0 -1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,0,1,0,2,2,1,1,1,2,1,1,0,-1,-1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,0,2,2,1,1,1,2,1,1,0,-1,-1,0] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,-1,0,1,3,0,0,1,1,1,0,1,0,1,1] |
| Phi of K* | [-2,-1,0,1,1,1,1,1,1,1,3,0,0,1,1,1,0,0,0,-1,-1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,2,2,1,1,1,0,1,1,2,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 2z^2+23z+39 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+23w^2z+39w |
| Inner characteristic polynomial | t^6+20t^4+28t^2+9 |
| Outer characteristic polynomial | t^7+28t^5+45t^3+16t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -448*K1**6 - 256*K1**4*K2**2 + 1568*K1**4*K2 - 4976*K1**4 + 640*K1**3*K2*K3 - 1472*K1**3*K3 - 4480*K1**2*K2**2 - 384*K1**2*K2*K4 + 10744*K1**2*K2 - 464*K1**2*K3**2 - 5460*K1**2 - 160*K1*K2**2*K3 + 6568*K1*K2*K3 + 512*K1*K3*K4 - 200*K2**4 + 296*K2**2*K4 - 4584*K2**2 - 1932*K3**2 - 166*K4**2 + 4652 |
| 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}, {1, 5}, {4}, {3}, {2}], [{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}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {3, 4}, {2}, {1}]] |
| If K is slice | False |