| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,-1,2,1,2,2,1,1,1,1,0,0,0,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.931'] |
| 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+26t^5+50t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.931'] |
| 2-strand cable arrow polynomial of the knot is: 160*K1**4*K2 - 2112*K1**4 - 480*K1**3*K3 - 816*K1**2*K2**2 - 192*K1**2*K2*K4 + 3192*K1**2*K2 - 1060*K1**2 + 1624*K1*K2*K3 + 192*K1*K3*K4 - 72*K2**4 + 184*K2**2*K4 - 1208*K2**2 - 508*K3**2 - 122*K4**2 + 1216 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.931'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13387', 'vk6.13472', 'vk6.13661', 'vk6.13767', 'vk6.13920', 'vk6.14015', 'vk6.14178', 'vk6.14200', 'vk6.14419', 'vk6.14445', 'vk6.14991', 'vk6.15112', 'vk6.15646', 'vk6.16102', 'vk6.16126', 'vk6.16752', 'vk6.16776', 'vk6.23165', 'vk6.23185', 'vk6.25390', 'vk6.25665', 'vk6.33142', 'vk6.33197', 'vk6.33739', 'vk6.33814', 'vk6.35147', 'vk6.35176', 'vk6.35203', 'vk6.37514', 'vk6.37762', 'vk6.42671', 'vk6.42686', 'vk6.42738', 'vk6.42791', 'vk6.44678', 'vk6.44716', 'vk6.53563', 'vk6.54955', 'vk6.56609', 'vk6.64587'] |
| 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 | O1O2O3O4U3U5O6O5U4U2U1U6 |
| R3 orbit | {'O1O2O3O4U3U5O6O5U4U2U1U6', 'O1O2O3U2O4U5O6O5U3U4U1U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U5U4U3U1O6O5U6U2 |
| Gauss code of K* | O1O2O3O4U3U2U5U1O5O6U4U6 |
| Gauss code of -K* | O1O2O3O4U5U1O5O6U4U6U3U2 |
| 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 1 2],[ 1 0 0 -1 1 1 2],[ 1 0 0 -1 1 1 1],[ 1 1 1 0 1 1 1],[ 0 -1 -1 -1 0 0 0],[-1 -1 -1 -1 0 0 2],[-2 -2 -1 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 -2 0 -1 -1 -2],[-1 2 0 0 -1 -1 -1],[ 0 0 0 0 -1 -1 -1],[ 1 1 1 1 0 1 1],[ 1 1 1 1 -1 0 0],[ 1 2 1 1 -1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,2,0,1,1,2,0,1,1,1,1,1,1,-1,-1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,-1,2,1,2,2,1,1,1,1,0,0,0,-1,0,1] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,-1,0,1,2,0,0,1,1,0,1,2,1,2,-1] |
| Phi of K* | [-2,-1,0,1,1,1,-1,2,1,2,2,1,1,1,1,0,0,0,-1,0,1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,1,1,1,1,1,1,1,1,1,2,0,0,2] |
| 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+18t^4+21t^2 |
| Outer characteristic polynomial | t^7+26t^5+50t^3+3t |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | 160*K1**4*K2 - 2112*K1**4 - 480*K1**3*K3 - 816*K1**2*K2**2 - 192*K1**2*K2*K4 + 3192*K1**2*K2 - 1060*K1**2 + 1624*K1*K2*K3 + 192*K1*K3*K4 - 72*K2**4 + 184*K2**2*K4 - 1208*K2**2 - 508*K3**2 - 122*K4**2 + 1216 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}]] |
| If K is slice | False |