| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,2,2,1,0,1,1,1,0,0,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1321'] |
| 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+28t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1321'] |
| 2-strand cable arrow polynomial of the knot is: -1312*K1**4 - 304*K1**2*K2**2 + 1264*K1**2*K2 + 140*K1**2 + 272*K1*K2*K3 - 8*K2**4 + 8*K2**2*K4 - 288*K2**2 - 60*K3**2 - 2*K4**2 + 288 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1321'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13900', 'vk6.13995', 'vk6.14169', 'vk6.14408', 'vk6.14975', 'vk6.15096', 'vk6.15641', 'vk6.16095', 'vk6.16716', 'vk6.16747', 'vk6.16840', 'vk6.18810', 'vk6.19286', 'vk6.19578', 'vk6.19923', 'vk6.21146', 'vk6.23154', 'vk6.23221', 'vk6.23393', 'vk6.25404', 'vk6.26473', 'vk6.26842', 'vk6.26858', 'vk6.33711', 'vk6.33786', 'vk6.34269', 'vk6.37529', 'vk6.38274', 'vk6.38290', 'vk6.38828', 'vk6.41021', 'vk6.42728', 'vk6.44693', 'vk6.45149', 'vk6.45157', 'vk6.45593', 'vk6.54120', 'vk6.54933', 'vk6.56412', 'vk6.56713', 'vk6.57796', 'vk6.58166', 'vk6.59357', 'vk6.59520', 'vk6.61125', 'vk6.62735', 'vk6.66404', 'vk6.69055'] |
| 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 | O1O2O3U4O5O6U3U1O4U6U5U2 |
| R3 orbit | {'O1O2U3O4O5U4O6U1U6O3U5U2', 'O1O2U3O4O5U6U1O3U5U4O6U2', 'O1O2O3U4O5O6U3U1O4U6U5U2'} |
| R3 orbit length | 3 |
| Gauss code of -K | O1O2O3U2U4U5O6U3U1O5O4U6 |
| Gauss code of K* | O1O2O3U4U3U5O6U2U1O5O4U6 |
| Gauss code of -K* | O1O2O3U4O5O6U3U2O4U6U1U5 |
| 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 1 -1 0 1 1],[ 2 0 2 0 1 2 1],[-1 -2 0 -1 0 0 0],[ 1 0 1 0 1 1 0],[ 0 -1 0 -1 0 0 1],[-1 -2 0 -1 0 0 0],[-1 -1 0 0 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 0 0 0 -1 -2],[-1 0 0 0 0 -1 -2],[-1 0 0 0 -1 0 -1],[ 0 0 0 1 0 -1 -1],[ 1 1 1 0 1 0 0],[ 2 2 2 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,0,0,0,1,2,0,0,1,2,1,0,1,1,1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,2,2,1,0,1,1,1,0,0,0,0,0] |
| Phi of -K | [-2,-1,0,1,1,1,1,1,1,1,2,0,1,1,2,1,1,0,0,0,0] |
| Phi of K* | [-1,-1,-1,0,1,2,0,0,0,2,2,0,1,1,1,1,1,1,0,1,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,1,1,2,2,1,0,1,1,1,0,0,0,0,0] |
| 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+15t^2 |
| Outer characteristic polynomial | t^7+22t^5+28t^3 |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | -1312*K1**4 - 304*K1**2*K2**2 + 1264*K1**2*K2 + 140*K1**2 + 272*K1*K2*K3 - 8*K2**4 + 8*K2**2*K4 - 288*K2**2 - 60*K3**2 - 2*K4**2 + 288 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {3, 5}, {1, 4}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{4, 6}, {5}, {1, 3}, {2}], [{4, 6}, {5}, {2, 3}, {1}], [{4, 6}, {5}, {3}, {1, 2}], [{4, 6}, {5}, {3}, {2}, {1}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |