| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,0,1,2,3,-1,0,0,0,0,1,0,1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1774'] |
| 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+23t^5+49t^3+14t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1774'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 768*K1**4*K2 - 3744*K1**4 + 736*K1**3*K2*K3 - 1152*K1**3*K3 + 128*K1**2*K2**3 - 3824*K1**2*K2**2 - 576*K1**2*K2*K4 + 8808*K1**2*K2 - 992*K1**2*K3**2 - 5500*K1**2 - 224*K1*K2**2*K3 + 7000*K1*K2*K3 + 1072*K1*K3*K4 - 104*K2**4 + 448*K2**2*K4 - 4608*K2**2 - 2308*K3**2 - 382*K4**2 + 4644 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1774'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3564', 'vk6.3586', 'vk6.3596', 'vk6.3807', 'vk6.3821', 'vk6.3840', 'vk6.3854', 'vk6.6981', 'vk6.6983', 'vk6.7014', 'vk6.7016', 'vk6.7199', 'vk6.7205', 'vk6.7231', 'vk6.15328', 'vk6.15351', 'vk6.15455', 'vk6.15476', 'vk6.33973', 'vk6.34019', 'vk6.34028', 'vk6.34430', 'vk6.48210', 'vk6.48236', 'vk6.48368', 'vk6.49951', 'vk6.49972', 'vk6.49990', 'vk6.53993', 'vk6.54012', 'vk6.54049', 'vk6.54493'] |
| 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 | O1O2O3U4U2O5O4U6U5O6U1U3 |
| R3 orbit | {'O1O2O3U4U2O5O4U6U5O6U1U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U3O4U5U4O6O5U2U6 |
| Gauss code of K* | O1O2U1O3O4U3U5U4O6O5U2U6 |
| Gauss code of -K* | O1O2U3O4O3U5U4O6O5U1U6U2 |
| 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 0 2 0 0 -1],[ 1 0 1 2 1 0 0],[ 0 -1 0 0 0 -1 0],[-2 -2 0 0 -1 0 -3],[ 0 -1 0 1 0 0 0],[ 0 0 1 0 0 0 0],[ 1 0 0 3 0 0 0]] |
| Primitive based matrix | [[ 0 2 0 0 0 -1 -1],[-2 0 0 0 -1 -2 -3],[ 0 0 0 1 0 0 0],[ 0 0 -1 0 0 -1 0],[ 0 1 0 0 0 -1 0],[ 1 2 0 1 1 0 0],[ 1 3 0 0 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,0,0,0,1,1,0,0,1,2,3,-1,0,0,0,0,1,0,1,0,0] |
| Phi over symmetry | [-2,0,0,0,1,1,0,0,1,2,3,-1,0,0,0,0,1,0,1,0,0] |
| Phi of -K | [-1,-1,0,0,0,2,0,0,0,1,1,1,1,1,0,0,0,1,1,2,2] |
| Phi of K* | [-2,0,0,0,1,1,1,2,2,0,1,0,0,1,0,-1,1,0,1,1,0] |
| Phi of -K* | [-1,-1,0,0,0,2,0,0,0,0,3,0,1,1,2,0,1,0,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 19z+39 |
| Enhanced Jones-Krushkal polynomial | 19w^2z+39w |
| Inner characteristic polynomial | t^6+17t^4+34t^2+9 |
| Outer characteristic polynomial | t^7+23t^5+49t^3+14t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 768*K1**4*K2 - 3744*K1**4 + 736*K1**3*K2*K3 - 1152*K1**3*K3 + 128*K1**2*K2**3 - 3824*K1**2*K2**2 - 576*K1**2*K2*K4 + 8808*K1**2*K2 - 992*K1**2*K3**2 - 5500*K1**2 - 224*K1*K2**2*K3 + 7000*K1*K2*K3 + 1072*K1*K3*K4 - 104*K2**4 + 448*K2**2*K4 - 4608*K2**2 - 2308*K3**2 - 382*K4**2 + 4644 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |