| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,2,1,1,3,0,0,1,2,2,2,0,1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1560'] |
| 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+38t^5+200t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1560'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 160*K1**4*K2 - 256*K1**4 + 224*K1**2*K2**3 - 864*K1**2*K2**2 + 1112*K1**2*K2 - 712*K1**2 + 488*K1*K2*K3 - 120*K2**4 + 16*K2**2*K4 - 360*K2**2 - 88*K3**2 - 2*K4**2 + 464 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1560'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4183', 'vk6.4264', 'vk6.5425', 'vk6.5545', 'vk6.7542', 'vk6.7624', 'vk6.9052', 'vk6.9133', 'vk6.18243', 'vk6.18580', 'vk6.24719', 'vk6.25134', 'vk6.36845', 'vk6.37310', 'vk6.44078', 'vk6.44419', 'vk6.48503', 'vk6.48584', 'vk6.49191', 'vk6.49301', 'vk6.50290', 'vk6.50364', 'vk6.51057', 'vk6.51090', 'vk6.56046', 'vk6.56322', 'vk6.60603', 'vk6.60948', 'vk6.65716', 'vk6.66012', 'vk6.68757', 'vk6.68967', 'vk6.73758', 'vk6.75704', 'vk6.78689', 'vk6.78691', 'vk6.78888', 'vk6.80314', 'vk6.81707', 'vk6.82457', 'vk6.83967', 'vk6.84445', 'vk6.86322', 'vk6.87090', 'vk6.87787', 'vk6.88111', 'vk6.88319', 'vk6.88400'] |
| 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 | O1O2O3U4O5U6U1O4O6U2U3U5 |
| R3 orbit | {'O1O2O3U4O5U2U6O4U1O6U3U5', 'O1O2O3U4O5U6U1O4O6U2U3U5', 'O1O2O3U4U5O4U6O5U1U2O6U3'} |
| R3 orbit length | 3 |
| Gauss code of -K | O1O2O3U4U1U2O5O6U3U5O4U6 |
| Gauss code of K* | O1O2O3U4U1U2O5U3O6O4U5U6 |
| Gauss code of -K* | O1O2O3U4U5O6O4U1O5U2U3U6 |
| 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 1 -1 2 0],[ 1 0 -1 0 1 1 2],[ 1 1 0 1 0 1 2],[-1 0 -1 0 -2 0 0],[ 1 -1 0 2 0 3 0],[-2 -1 -1 0 -3 0 -2],[ 0 -2 -2 0 0 2 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 0 -2 -1 -1 -3],[-1 0 0 0 0 -1 -2],[ 0 2 0 0 -2 -2 0],[ 1 1 0 2 0 -1 1],[ 1 1 1 2 1 0 0],[ 1 3 2 0 -1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,0,2,1,1,3,0,0,1,2,2,2,0,1,-1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,2,1,1,3,0,0,1,2,2,2,0,1,-1,0] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,-1,1,2,-1,-1,2,2,1,0,0,1,0,1] |
| Phi of K* | [-2,-1,0,1,1,1,1,0,0,2,2,1,0,1,2,1,-1,-1,0,-1,1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,2,3,-1,2,0,1,2,1,1,0,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 5z+11 |
| Enhanced Jones-Krushkal polynomial | -4w^3z+9w^2z+11w |
| Inner characteristic polynomial | t^6+30t^4+147t^2 |
| Outer characteristic polynomial | t^7+38t^5+200t^3 |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 160*K1**4*K2 - 256*K1**4 + 224*K1**2*K2**3 - 864*K1**2*K2**2 + 1112*K1**2*K2 - 712*K1**2 + 488*K1*K2*K3 - 120*K2**4 + 16*K2**2*K4 - 360*K2**2 - 88*K3**2 - 2*K4**2 + 464 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |