| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-2,1,1,3,3,1,0,2,1,0,1,1,-1,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1469'] |
| 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+51t^5+29t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1469'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 - 192*K1**4*K2**2 + 2368*K1**4*K2 - 8304*K1**4 + 224*K1**3*K2*K3 - 1632*K1**3*K3 + 128*K1**2*K2**3 - 3136*K1**2*K2**2 - 96*K1**2*K2*K4 + 12128*K1**2*K2 - 176*K1**2*K3**2 - 3872*K1**2 + 3280*K1*K2*K3 + 152*K1*K3*K4 - 104*K2**4 + 56*K2**2*K4 - 3912*K2**2 - 744*K3**2 - 42*K4**2 + 4000 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1469'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3669', 'vk6.3766', 'vk6.3955', 'vk6.4052', 'vk6.4499', 'vk6.4596', 'vk6.5885', 'vk6.6014', 'vk6.7154', 'vk6.7327', 'vk6.7420', 'vk6.7930', 'vk6.8051', 'vk6.9364', 'vk6.17907', 'vk6.18002', 'vk6.18743', 'vk6.24442', 'vk6.24868', 'vk6.25329', 'vk6.37482', 'vk6.43869', 'vk6.44215', 'vk6.44518', 'vk6.48293', 'vk6.48358', 'vk6.50076', 'vk6.50186', 'vk6.50575', 'vk6.50640', 'vk6.55866', 'vk6.60723'] |
| 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 | O1O2O3U1O4U3O5U6U5U4O6U2 |
| R3 orbit | {'O1O2O3U1O4U3O5U6U5U4O6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2O4U5U6U4O6U1O5U3 |
| Gauss code of K* | O1O2O3U1O4U5U4U6O5U3O6U2 |
| Gauss code of -K* | O1O2O3U2O4U1O5U4U6U5O6U3 |
| 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 0 2 1 -2],[ 2 0 2 1 1 0 2],[-1 -2 0 -1 2 1 -3],[ 0 -1 1 0 1 0 -1],[-2 -1 -2 -1 0 0 -3],[-1 0 -1 0 0 0 -1],[ 2 -2 3 1 3 1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 0 -2 -1 -1 -3],[-1 0 0 -1 0 0 -1],[-1 2 1 0 -1 -2 -3],[ 0 1 0 1 0 -1 -1],[ 2 1 0 2 1 0 2],[ 2 3 1 3 1 -2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,0,2,1,1,3,1,0,0,1,1,2,3,1,1,-2] |
| Phi over symmetry | [-2,-2,0,1,1,2,-2,1,1,3,3,1,0,2,1,0,1,1,-1,-1,1] |
| Phi of -K | [-2,-2,0,1,1,2,-2,1,1,3,3,1,0,2,1,0,1,1,-1,-1,1] |
| Phi of K* | [-2,-1,-1,0,2,2,-1,1,1,1,3,1,0,0,1,1,2,3,1,1,-2] |
| Phi of -K* | [-2,-2,0,1,1,2,-2,1,1,3,3,1,0,2,1,0,1,1,-1,0,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 21z+43 |
| Enhanced Jones-Krushkal polynomial | 21w^2z+43w |
| Inner characteristic polynomial | t^6+37t^4+18t^2+1 |
| Outer characteristic polynomial | t^7+51t^5+29t^3+3t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -128*K1**6 - 192*K1**4*K2**2 + 2368*K1**4*K2 - 8304*K1**4 + 224*K1**3*K2*K3 - 1632*K1**3*K3 + 128*K1**2*K2**3 - 3136*K1**2*K2**2 - 96*K1**2*K2*K4 + 12128*K1**2*K2 - 176*K1**2*K3**2 - 3872*K1**2 + 3280*K1*K2*K3 + 152*K1*K3*K4 - 104*K2**4 + 56*K2**2*K4 - 3912*K2**2 - 744*K3**2 - 42*K4**2 + 4000 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {4, 5}, {1, 2}], [{6}, {4, 5}, {2, 3}, {1}]] |
| If K is slice | False |