| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,-1,1,1,2,2,1,0,1,1,0,0,0,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1078'] |
| 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+22t^5+18t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1078'] |
| 2-strand cable arrow polynomial of the knot is: -240*K1**4 - 128*K1**2*K2**2 + 408*K1**2*K2 - 80*K1**2*K3**2 - 304*K1**2 + 408*K1*K2*K3 + 136*K1*K3*K4 - 8*K2**4 + 16*K2**2*K4 - 272*K2**2 - 200*K3**2 - 54*K4**2 + 316 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1078'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4420', 'vk6.4515', 'vk6.5806', 'vk6.5933', 'vk6.7865', 'vk6.7970', 'vk6.9285', 'vk6.9404', 'vk6.10167', 'vk6.10238', 'vk6.10381', 'vk6.11238', 'vk6.12501', 'vk6.12612', 'vk6.17882', 'vk6.17947', 'vk6.18218', 'vk6.18294', 'vk6.18555', 'vk6.18629', 'vk6.24385', 'vk6.24681', 'vk6.24685', 'vk6.25102', 'vk6.30050', 'vk6.30111', 'vk6.30918', 'vk6.30920', 'vk6.31041', 'vk6.31043', 'vk6.32104', 'vk6.32106', 'vk6.32223', 'vk6.32225', 'vk6.36812', 'vk6.36912', 'vk6.37269', 'vk6.37273', 'vk6.37370', 'vk6.43812', 'vk6.44053', 'vk6.44129', 'vk6.50591', 'vk6.51986', 'vk6.51988', 'vk6.52081', 'vk6.52083', 'vk6.52867', 'vk6.52914', 'vk6.55835', 'vk6.56287', 'vk6.60555', 'vk6.65962', 'vk6.65966', 'vk6.78907', 'vk6.78923'] |
| 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 | O1O2O3O4U5U4O6U2O5U6U1U3 |
| R3 orbit | {'O1O2O3U4U5U2O6O4U1U6O5U3', 'O1O2O3O4U5U4O6U2O5U6U1U3', 'O1O2O3O4U5U4U1O6O5U2U6U3', 'O1O2O3U4U5U2O5O6U1O4U6U3'} |
| R3 orbit length | 4 |
| Gauss code of -K | O1O2O3O4U2U4U5O6U3O5U1U6 |
| Gauss code of K* | O1O2O3U2U4U3U5O6O5U1O4U6 |
| Gauss code of -K* | O1O2O3U4O5U3O6O4U6U1U5U2 |
| 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 -1 -1 2 1 -1 0],[ 1 0 0 2 1 0 0],[ 1 0 0 1 0 0 0],[-2 -2 -1 0 1 -2 -1],[-1 -1 0 -1 0 -1 -1],[ 1 0 0 2 1 0 0],[ 0 0 0 1 1 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 1 -1 -1 -2 -2],[-1 -1 0 -1 0 -1 -1],[ 0 1 1 0 0 0 0],[ 1 1 0 0 0 0 0],[ 1 2 1 0 0 0 0],[ 1 2 1 0 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,-1,1,1,2,2,1,0,1,1,0,0,0,0,0,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,-1,1,1,2,2,1,0,1,1,0,0,0,0,0,0] |
| Phi of -K | [-1,-1,-1,0,1,2,0,0,1,1,1,0,1,1,1,1,2,2,0,1,2] |
| Phi of K* | [-2,-1,0,1,1,1,2,1,1,1,2,0,1,1,2,1,1,1,0,0,0] |
| Phi of -K* | [-1,-1,-1,0,1,2,0,0,0,0,1,0,0,1,2,0,1,2,1,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 7z+15 |
| Enhanced Jones-Krushkal polynomial | 7w^2z+15w |
| Inner characteristic polynomial | t^6+14t^4+5t^2 |
| Outer characteristic polynomial | t^7+22t^5+18t^3 |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | -240*K1**4 - 128*K1**2*K2**2 + 408*K1**2*K2 - 80*K1**2*K3**2 - 304*K1**2 + 408*K1*K2*K3 + 136*K1*K3*K4 - 8*K2**4 + 16*K2**2*K4 - 272*K2**2 - 200*K3**2 - 54*K4**2 + 316 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {5}, {3, 4}, {1}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {3, 5}, {1, 2}]] |
| If K is slice | False |