| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,0,0,2,2,1,0,2,2,2,0,0,1,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.946'] |
| Arrow polynomial of the knot is: -2*K1**2 + K2 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['4.6', '4.8', '6.780', '6.804', '6.914', '6.931', '6.946', '6.960', '6.1002', '6.1016', '6.1019', '6.1051', '6.1058', '6.1078', '6.1102', '6.1115', '6.1217', '6.1294', '6.1306', '6.1317', '6.1321', '6.1324', '6.1336', '6.1377', '6.1416', '6.1420', '6.1427', '6.1429', '6.1434', '6.1436', '6.1437', '6.1439', '6.1441', '6.1444', '6.1450', '6.1451', '6.1458', '6.1459', '6.1477', '6.1482', '6.1490', '6.1503', '6.1504', '6.1511', '6.1521', '6.1547', '6.1560', '6.1561', '6.1562', '6.1597', '6.1598', '6.1600', '6.1601', '6.1608', '6.1620', '6.1622', '6.1624', '6.1634', '6.1635', '6.1637', '6.1638', '6.1713', '6.1725', '6.1758', '6.1846', '6.1933', '6.1944', '6.1949', '6.1950', '6.1951'] |
| Outer characteristic polynomial of the knot is: t^7+43t^5+68t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.946'] |
| 2-strand cable arrow polynomial of the knot is: -352*K1**4 + 32*K1**3*K2*K3 - 208*K1**2*K2**2 + 568*K1**2*K2 - 224*K1**2*K3**2 - 524*K1**2 + 776*K1*K2*K3 + 336*K1*K3*K4 - 8*K2**4 + 16*K2**2*K4 - 448*K2**2 - 404*K3**2 - 122*K4**2 + 560 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.946'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16520', 'vk6.16611', 'vk6.18087', 'vk6.18423', 'vk6.22951', 'vk6.23046', 'vk6.24534', 'vk6.24951', 'vk6.34918', 'vk6.35027', 'vk6.36677', 'vk6.37099', 'vk6.42489', 'vk6.42600', 'vk6.43953', 'vk6.44268', 'vk6.54747', 'vk6.54842', 'vk6.55903', 'vk6.56187', 'vk6.59211', 'vk6.59274', 'vk6.60429', 'vk6.60782', 'vk6.64757', 'vk6.64816', 'vk6.65545', 'vk6.65855', 'vk6.68055', 'vk6.68118', 'vk6.68623', 'vk6.68836', 'vk6.71378', 'vk6.71437', 'vk6.71904', 'vk6.71963', 'vk6.72827', 'vk6.74422', 'vk6.76611', 'vk6.77043', 'vk6.77766', 'vk6.78479', 'vk6.78636', 'vk6.78831', 'vk6.85144', 'vk6.87219', 'vk6.89278', 'vk6.89426'] |
| 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 | O1O2O3O4U5U1O6O5U2U4U6U3 |
| R3 orbit | {'O1O2O3U4O5U1O4O6U2U6U5U3', 'O1O2O3O4U2U5O6U1O5U4U6U3', 'O1O2O3O4U5U1O6O5U2U4U6U3'} |
| R3 orbit length | 3 |
| Gauss code of -K | O1O2O3O4U2U5U1U3O6O5U4U6 |
| Gauss code of K* | O1O2O3O4U5U1U4U2O6O5U3U6 |
| Gauss code of -K* | O1O2O3O4U5U2O6O5U3U1U4U6 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -2 2 1 0 1],[ 2 0 0 2 1 2 1],[ 2 0 0 3 1 2 1],[-2 -2 -3 0 -1 -1 0],[-1 -1 -1 1 0 -1 0],[ 0 -2 -2 1 1 0 1],[-1 -1 -1 0 0 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 0 -1 -1 -2 -3],[-1 0 0 0 -1 -1 -1],[-1 1 0 0 -1 -1 -1],[ 0 1 1 1 0 -2 -2],[ 2 2 1 1 2 0 0],[ 2 3 1 1 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,0,1,1,2,3,0,1,1,1,1,1,1,2,2,0] |
| Phi over symmetry | [-2,-2,0,1,1,2,0,0,2,2,1,0,2,2,2,0,0,1,0,0,1] |
| Phi of -K | [-2,-2,0,1,1,2,0,0,2,2,1,0,2,2,2,0,0,1,0,0,1] |
| Phi of K* | [-2,-1,-1,0,2,2,0,1,1,1,2,0,0,2,2,0,2,2,0,0,0] |
| Phi of -K* | [-2,-2,0,1,1,2,0,2,1,1,2,2,1,1,3,1,1,1,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 9z+19 |
| Enhanced Jones-Krushkal polynomial | 9w^2z+19w |
| Inner characteristic polynomial | t^6+29t^4+39t^2 |
| Outer characteristic polynomial | t^7+43t^5+68t^3 |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | -352*K1**4 + 32*K1**3*K2*K3 - 208*K1**2*K2**2 + 568*K1**2*K2 - 224*K1**2*K3**2 - 524*K1**2 + 776*K1*K2*K3 + 336*K1*K3*K4 - 8*K2**4 + 16*K2**2*K4 - 448*K2**2 - 404*K3**2 - 122*K4**2 + 560 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {3, 5}, {1, 4}], [{4, 6}, {1, 5}, {2, 3}], [{5, 6}, {1, 4}, {2, 3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {4, 5}, {2, 3}, {1}]] |
| If K is slice | False |