| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,0,0,2,2,1,1,2,2,2,0,0,0,0,1,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.1102'] |
| 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+32t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1102'] |
| 2-strand cable arrow polynomial of the knot is: 128*K1**4*K2 - 1120*K1**4 - 448*K1**3*K3 - 400*K1**2*K2**2 + 2680*K1**2*K2 - 1636*K1**2 - 32*K1*K2**2*K3 + 1192*K1*K2*K3 + 56*K1*K3*K4 - 72*K2**4 + 128*K2**2*K4 - 1224*K2**2 - 420*K3**2 - 66*K4**2 + 1232 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1102'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.14102', 'vk6.14112', 'vk6.14309', 'vk6.14329', 'vk6.15540', 'vk6.15560', 'vk6.16026', 'vk6.16036', 'vk6.16435', 'vk6.16446', 'vk6.16452', 'vk6.22841', 'vk6.22851', 'vk6.34056', 'vk6.34113', 'vk6.34452', 'vk6.34494', 'vk6.34789', 'vk6.34810', 'vk6.34824', 'vk6.42404', 'vk6.42422', 'vk6.54075', 'vk6.54085', 'vk6.54299', 'vk6.54319', 'vk6.54672', 'vk6.54693', 'vk6.54707', 'vk6.64533', 'vk6.64539', 'vk6.64740', 'vk6.75247', 'vk6.75263', 'vk6.78459', 'vk6.78475', 'vk6.85760', 'vk6.87684', 'vk6.89631', 'vk6.90072'] |
| 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 | O1O2O3O4U2U1O5U3U5O6U4U6 |
| R3 orbit | {'O1O2O3O4U2U1O5U3U5O6U4U6', 'O1O2O3U1O4U5U2O6U4U3O5U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U5U1O5U6U2O6U4U3 |
| Gauss code of K* | O1O2U3O4O3U5O6O5U2U1U4U6 |
| Gauss code of -K* | O1O2U1O3O4U3O5O6U2U4U6U5 |
| 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 -2 0 2 1 1],[ 2 0 0 2 3 1 1],[ 2 0 0 1 2 1 1],[ 0 -2 -1 0 2 1 1],[-2 -3 -2 -2 0 0 1],[-1 -1 -1 -1 0 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 1 0 -2 -2 -3],[-1 -1 0 0 -1 -1 -1],[-1 0 0 0 -1 -1 -1],[ 0 2 1 1 0 -1 -2],[ 2 2 1 1 1 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,-1,0,2,2,3,0,1,1,1,1,1,1,1,2,0] |
| Phi over symmetry | [-2,-2,0,1,1,2,0,0,2,2,1,1,2,2,2,0,0,0,0,1,2] |
| Phi of -K | [-2,-2,0,1,1,2,0,0,2,2,1,1,2,2,2,0,0,0,0,1,2] |
| Phi of K* | [-2,-1,-1,0,2,2,1,2,0,1,2,0,0,2,2,0,2,2,0,1,0] |
| Phi of -K* | [-2,-2,0,1,1,2,0,1,1,1,2,2,1,1,3,1,1,2,0,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 2z^2+15z+23 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+15w^2z+23w |
| Inner characteristic polynomial | t^6+29t^4+11t^2+1 |
| Outer characteristic polynomial | t^7+43t^5+32t^3+4t |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | 128*K1**4*K2 - 1120*K1**4 - 448*K1**3*K3 - 400*K1**2*K2**2 + 2680*K1**2*K2 - 1636*K1**2 - 32*K1*K2**2*K3 + 1192*K1*K2*K3 + 56*K1*K3*K4 - 72*K2**4 + 128*K2**2*K4 - 1224*K2**2 - 420*K3**2 - 66*K4**2 + 1232 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {5}, {4}, {2, 3}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |