| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,2,2,-1,1,0,1,1,0,0,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.804'] |
| 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+24t^5+67t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.804'] |
| 2-strand cable arrow polynomial of the knot is: 320*K1**4*K2 - 2368*K1**4 - 640*K1**3*K3 - 1776*K1**2*K2**2 - 448*K1**2*K2*K4 + 5960*K1**2*K2 - 3804*K1**2 + 3480*K1*K2*K3 + 456*K1*K3*K4 - 40*K2**4 + 320*K2**2*K4 - 2976*K2**2 - 1180*K3**2 - 266*K4**2 + 2960 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.804'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4866', 'vk6.5209', 'vk6.6444', 'vk6.6863', 'vk6.8405', 'vk6.8824', 'vk6.9761', 'vk6.10052', 'vk6.11669', 'vk6.12020', 'vk6.13011', 'vk6.20501', 'vk6.20776', 'vk6.21868', 'vk6.27911', 'vk6.29407', 'vk6.29743', 'vk6.32662', 'vk6.33003', 'vk6.39342', 'vk6.39808', 'vk6.46372', 'vk6.47610', 'vk6.47947', 'vk6.48832', 'vk6.49101', 'vk6.51351', 'vk6.51562', 'vk6.53272', 'vk6.57362', 'vk6.64341', 'vk6.66919'] |
| 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 | O1O2O3O4U5O6U4U6U1O5U3U2 |
| R3 orbit | {'O1O2O3O4U5O6U4U6U1O5U3U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U3U2O5U4U6U1O6U5 |
| Gauss code of K* | O1O2O3U4O5O6U3U6U5U1O4U2 |
| Gauss code of -K* | O1O2O3U2O4U3U5U6U1O6O5U4 |
| 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 1 1 0 -2 1],[ 1 0 1 0 -1 0 1],[-1 -1 0 0 0 -2 1],[-1 0 0 0 0 -2 1],[ 0 1 0 0 0 -1 1],[ 2 0 2 2 1 0 1],[-1 -1 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 0 0 -2],[-1 -1 0 -1 -1 -1 -1],[-1 0 1 0 0 -1 -2],[ 0 0 1 0 0 1 -1],[ 1 0 1 1 -1 0 0],[ 2 2 1 2 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,0,0,2,1,1,1,1,0,1,2,-1,1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,2,2,-1,1,0,1,1,0,0,-1,-1,0] |
| Phi of -K | [-2,-1,0,1,1,1,1,1,1,1,2,2,1,2,1,1,1,0,0,-1,-1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,-1,0,1,2,0,1,1,1,1,2,1,2,1,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,1,1,2,2,-1,1,0,1,1,0,0,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 4z^2+21z+27 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2-4w^3z+25w^2z+27w |
| Inner characteristic polynomial | t^6+16t^4+34t^2+1 |
| Outer characteristic polynomial | t^7+24t^5+67t^3+9t |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | 320*K1**4*K2 - 2368*K1**4 - 640*K1**3*K3 - 1776*K1**2*K2**2 - 448*K1**2*K2*K4 + 5960*K1**2*K2 - 3804*K1**2 + 3480*K1*K2*K3 + 456*K1*K3*K4 - 40*K2**4 + 320*K2**2*K4 - 2976*K2**2 - 1180*K3**2 - 266*K4**2 + 2960 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}]] |
| If K is slice | False |