| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,2,1,1,2,1,1,1,1,1,2,1,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.914'] |
| 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+30t^5+23t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.914'] |
| 2-strand cable arrow polynomial of the knot is: 224*K1**4*K2 - 1120*K1**4 - 32*K1**3*K3 - 1456*K1**2*K2**2 + 2520*K1**2*K2 - 1052*K1**2 + 1144*K1*K2*K3 - 72*K2**4 + 72*K2**2*K4 - 912*K2**2 - 228*K3**2 - 18*K4**2 + 928 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.914'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11499', 'vk6.11813', 'vk6.12827', 'vk6.13154', 'vk6.13397', 'vk6.13492', 'vk6.13681', 'vk6.13777', 'vk6.14210', 'vk6.14465', 'vk6.15688', 'vk6.16136', 'vk6.16760', 'vk6.16772', 'vk6.16878', 'vk6.19046', 'vk6.19314', 'vk6.19609', 'vk6.22482', 'vk6.23177', 'vk6.23263', 'vk6.23786', 'vk6.26504', 'vk6.28379', 'vk6.33148', 'vk6.33209', 'vk6.33302', 'vk6.35168', 'vk6.36031', 'vk6.40033', 'vk6.40291', 'vk6.42667', 'vk6.42682', 'vk6.44734', 'vk6.46758', 'vk6.48013', 'vk6.52254', 'vk6.53409', 'vk6.53573', 'vk6.53701'] |
| 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 | O1O2O3O4U3U1O5O6U4U6U5U2 |
| R3 orbit | {'O1O2O3O4U3U1O5O6U4U6U5U2', 'O1O2O3U4U1O5O6U3U6U5O4U2'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U3U5U6U1O6O5U4U2 |
| Gauss code of K* | O1O2O3O4U5U4U6U1O6O5U3U2 |
| Gauss code of -K* | O1O2O3O4U3U2O5O6U4U6U1U5 |
| 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 1 -1 0 1 1],[ 2 0 2 0 2 1 1],[-1 -2 0 -1 -1 1 1],[ 1 0 1 0 1 1 1],[ 0 -2 1 -1 0 2 1],[-1 -1 -1 -1 -2 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 1 -1 -1 -2],[-1 -1 0 0 -1 -1 -1],[-1 -1 0 0 -2 -1 -1],[ 0 1 1 2 0 -1 -2],[ 1 1 1 1 1 0 0],[ 2 2 1 1 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,-1,1,1,2,0,1,1,1,2,1,1,1,2,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,2,1,1,2,1,1,1,1,1,2,1,0,-1,-1] |
| Phi of -K | [-2,-1,0,1,1,1,1,0,1,2,2,0,1,1,1,0,-1,0,-1,-1,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,-1,1,2,1,0,1,1,0,1,2,0,0,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,2,1,1,2,1,1,1,1,1,2,1,0,-1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 4z^2+17z+19 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+17w^2z+19w |
| Inner characteristic polynomial | t^6+22t^4+10t^2+1 |
| Outer characteristic polynomial | t^7+30t^5+23t^3+4t |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | 224*K1**4*K2 - 1120*K1**4 - 32*K1**3*K3 - 1456*K1**2*K2**2 + 2520*K1**2*K2 - 1052*K1**2 + 1144*K1*K2*K3 - 72*K2**4 + 72*K2**2*K4 - 912*K2**2 - 228*K3**2 - 18*K4**2 + 928 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}], [{6}, {4, 5}, {3}, {1, 2}]] |
| If K is slice | False |