| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,0,0,2,2,1,-1,-1,0,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1561'] |
| 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+34t^5+200t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1561'] |
| 2-strand cable arrow polynomial of the knot is: -240*K1**4 - 192*K1**2*K2**2 + 632*K1**2*K2 - 80*K1**2*K3**2 - 656*K1**2 + 760*K1*K2*K3 + 136*K1*K3*K4 - 8*K2**4 + 16*K2**2*K4 - 528*K2**2 - 360*K3**2 - 54*K4**2 + 572 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1561'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71589', 'vk6.71592', 'vk6.71714', 'vk6.71718', 'vk6.72134', 'vk6.72137', 'vk6.72330', 'vk6.73778', 'vk6.73798', 'vk6.73917', 'vk6.73932', 'vk6.75743', 'vk6.75917', 'vk6.75919', 'vk6.77205', 'vk6.77215', 'vk6.77518', 'vk6.77527', 'vk6.78710', 'vk6.78720', 'vk6.78756', 'vk6.78912', 'vk6.78926', 'vk6.79049', 'vk6.79616', 'vk6.80331', 'vk6.80337', 'vk6.80359', 'vk6.80455', 'vk6.80461', 'vk6.80572', 'vk6.81024', 'vk6.81347', 'vk6.81717', 'vk6.84457', 'vk6.85429', 'vk6.87987', 'vk6.88358', 'vk6.88365', 'vk6.89313'] |
| 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 | O1O2O3U4O5U6U1O4O6U2U5U3 |
| R3 orbit | {'O1O2O3U4O5U2U6O4U1O6U5U3', 'O1O2O3U4O5U6U1O4O6U2U5U3'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3U1U4U2O5O6U3U5O4U6 |
| Gauss code of K* | O1O2O3U4U1U3O5U2O6O4U5U6 |
| Gauss code of -K* | O1O2O3U4U5O6O4U2O5U1U3U6 |
| 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 -1 1 1 0 2],[ 1 1 0 2 0 0 2],[-2 -1 -2 0 -2 -1 -1],[ 1 -1 0 2 0 2 0],[-1 0 0 1 -2 0 -1],[ 0 -2 -2 1 0 1 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 -1 -1 -1 -2 -2],[-1 1 0 -1 0 0 -2],[ 0 1 1 0 -2 -2 0],[ 1 1 0 2 0 -1 1],[ 1 2 0 2 1 0 0],[ 1 2 2 0 -1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,1,1,1,2,2,1,0,0,2,2,2,0,1,-1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,0,0,2,2,1,-1,-1,0,-1,1] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,-1,2,1,-1,-1,2,2,1,0,1,0,1,0] |
| Phi of K* | [-2,-1,0,1,1,1,0,1,1,1,2,0,0,2,2,1,-1,-1,0,-1,1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,2,2,-1,2,0,1,2,0,2,1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 7z+15 |
| Enhanced Jones-Krushkal polynomial | -4w^3z+11w^2z+15w |
| Inner characteristic polynomial | t^6+26t^4+135t^2 |
| Outer characteristic polynomial | t^7+34t^5+200t^3 |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | -240*K1**4 - 192*K1**2*K2**2 + 632*K1**2*K2 - 80*K1**2*K3**2 - 656*K1**2 + 760*K1*K2*K3 + 136*K1*K3*K4 - 8*K2**4 + 16*K2**2*K4 - 528*K2**2 - 360*K3**2 - 54*K4**2 + 572 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |