| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,1,1,2,2,0,1,0,1,0,0,0,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1889'] |
| 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+21t^5+34t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1889', '7.35266'] |
| 2-strand cable arrow polynomial of the knot is: 128*K1**4*K2 - 3376*K1**4 + 192*K1**3*K2*K3 - 992*K1**3*K3 + 32*K1**2*K2**3 - 2928*K1**2*K2**2 - 384*K1**2*K2*K4 + 8360*K1**2*K2 - 336*K1**2*K3**2 - 4564*K1**2 - 32*K1*K2**2*K3 + 4760*K1*K2*K3 + 536*K1*K3*K4 - 120*K2**4 + 248*K2**2*K4 - 3520*K2**2 - 1396*K3**2 - 202*K4**2 + 3592 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1889'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73287', 'vk6.73301', 'vk6.73430', 'vk6.73444', 'vk6.74094', 'vk6.74099', 'vk6.74665', 'vk6.74668', 'vk6.75434', 'vk6.75444', 'vk6.76132', 'vk6.76137', 'vk6.78160', 'vk6.78182', 'vk6.78392', 'vk6.78414', 'vk6.79096', 'vk6.79109', 'vk6.79985', 'vk6.80003', 'vk6.80138', 'vk6.80156', 'vk6.80604', 'vk6.80617', 'vk6.83806', 'vk6.83819', 'vk6.85118', 'vk6.85131', 'vk6.86608', 'vk6.86621', 'vk6.87385', 'vk6.87399'] |
| 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 | O1O2O3U1U4O5U2O6U3O4U6U5 |
| R3 orbit | {'O1O2O3U1U4O5U2O6U3O4U6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O6U1O5U2O4U6U3 |
| Gauss code of K* | O1O2U3O4U5O6U2O5O3U1U4U6 |
| Gauss code of -K* | O1O2U3O4U2O5U1O3O6U4U5U6 |
| 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 0 2 1],[ 0 -1 0 1 -1 1 0],[-1 -2 -1 0 -1 1 0],[ 0 0 1 1 0 0 0],[-1 -2 -1 -1 0 0 0],[ 0 -1 0 0 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 0 -2],[-1 0 1 0 -1 -1 -2],[-1 -1 0 0 0 -1 -2],[ 0 0 0 0 0 0 -1],[ 0 1 0 0 0 1 0],[ 0 1 1 0 -1 0 -1],[ 2 2 2 1 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,0,2,-1,0,1,1,2,0,0,1,2,0,0,1,-1,0,1] |
| Phi over symmetry | [-2,0,0,0,1,1,0,1,1,2,2,0,1,0,1,0,0,0,1,1,-1] |
| Phi of -K | [-2,0,0,0,1,1,1,1,2,1,1,0,0,1,1,1,0,0,0,1,-1] |
| Phi of K* | [-1,-1,0,0,0,2,-1,0,1,1,1,0,0,1,1,-1,0,1,0,2,1] |
| Phi of -K* | [-2,0,0,0,1,1,0,1,1,2,2,0,1,0,1,0,0,0,1,1,-1] |
| 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+15t^4+15t^2 |
| Outer characteristic polynomial | t^7+21t^5+34t^3+4t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | 128*K1**4*K2 - 3376*K1**4 + 192*K1**3*K2*K3 - 992*K1**3*K3 + 32*K1**2*K2**3 - 2928*K1**2*K2**2 - 384*K1**2*K2*K4 + 8360*K1**2*K2 - 336*K1**2*K3**2 - 4564*K1**2 - 32*K1*K2**2*K3 + 4760*K1*K2*K3 + 536*K1*K3*K4 - 120*K2**4 + 248*K2**2*K4 - 3520*K2**2 - 1396*K3**2 - 202*K4**2 + 3592 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {5}, {1, 4}, {2}]] |
| If K is slice | False |