| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,2,3,0,1,1,1,1,0,0,-1,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1432'] |
| Arrow polynomial of the knot is: -6*K1**2 + 3*K2 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.689', '6.691', '6.752', '6.754', '6.1106', '6.1116', '6.1126', '6.1335', '6.1379', '6.1386', '6.1409', '6.1415', '6.1417', '6.1418', '6.1421', '6.1422', '6.1428', '6.1431', '6.1432', '6.1435', '6.1443', '6.1445', '6.1446', '6.1447', '6.1454', '6.1455', '6.1460', '6.1462', '6.1464', '6.1466', '6.1472', '6.1474', '6.1475', '6.1501', '6.1516', '6.1518', '6.1566', '6.1570', '6.1590', '6.1599', '6.1602', '6.1603', '6.1604', '6.1605', '6.1614', '6.1615', '6.1625', '6.1628', '6.1730', '6.1780', '6.1883', '6.1885', '6.1888', '6.1890', '6.1941', '6.1943', '6.1945', '6.1948', '6.1961', '6.1963', '6.1966', '6.1967', '6.1971'] |
| Outer characteristic polynomial of the knot is: t^7+24t^5+23t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1432'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**6 + 1440*K1**4*K2 - 5712*K1**4 + 32*K1**3*K2*K3 - 416*K1**3*K3 - 2720*K1**2*K2**2 + 7960*K1**2*K2 - 48*K1**2*K3**2 - 1928*K1**2 + 2008*K1*K2*K3 + 24*K1*K3*K4 - 24*K2**4 + 40*K2**2*K4 - 2528*K2**2 - 384*K3**2 - 18*K4**2 + 2528 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1432'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4817', 'vk6.5161', 'vk6.6376', 'vk6.6807', 'vk6.8345', 'vk6.8779', 'vk6.9715', 'vk6.10019', 'vk6.11613', 'vk6.11964', 'vk6.12955', 'vk6.20471', 'vk6.20736', 'vk6.21824', 'vk6.27859', 'vk6.29367', 'vk6.31424', 'vk6.32598', 'vk6.39293', 'vk6.39768', 'vk6.41471', 'vk6.46332', 'vk6.47594', 'vk6.47907', 'vk6.49055', 'vk6.49881', 'vk6.51313', 'vk6.51531', 'vk6.53220', 'vk6.57330', 'vk6.62020', 'vk6.64309'] |
| 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 | O1O2O3U2O4U3O5U6U1O6U4U5 |
| R3 orbit | {'O1O2O3U2O4U3O5U6U1O6U4U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O6U3U6O4U1O5U2 |
| Gauss code of K* | O1O2U1O3O4U2U5U6O5U3O6U4 |
| Gauss code of -K* | O1O2U3O4O3U1O5U2O6U5U6U4 |
| 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 0 1 2 -1],[ 1 0 -1 1 1 1 1],[ 1 1 0 1 1 0 1],[ 0 -1 -1 0 1 1 0],[-1 -1 -1 -1 0 1 -1],[-2 -1 0 -1 -1 0 -2],[ 1 -1 -1 0 1 2 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 -1 -1 0 -1 -2],[-1 1 0 -1 -1 -1 -1],[ 0 1 1 0 -1 -1 0],[ 1 0 1 1 0 1 1],[ 1 1 1 1 -1 0 1],[ 1 2 1 0 -1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,1,1,0,1,2,1,1,1,1,1,1,0,-1,-1,-1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,2,3,0,1,1,1,1,0,0,-1,-1,-1] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,-1,0,1,3,-1,0,1,2,1,1,1,0,1,0] |
| Phi of K* | [-2,-1,0,1,1,1,0,1,1,2,3,0,1,1,1,1,0,0,-1,-1,-1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,-1,0,1,2,-1,1,1,1,1,1,0,1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+16t^4+8t^2+1 |
| Outer characteristic polynomial | t^7+24t^5+23t^3+4t |
| Flat arrow polynomial | -6*K1**2 + 3*K2 + 4 |
| 2-strand cable arrow polynomial | -256*K1**6 + 1440*K1**4*K2 - 5712*K1**4 + 32*K1**3*K2*K3 - 416*K1**3*K3 - 2720*K1**2*K2**2 + 7960*K1**2*K2 - 48*K1**2*K3**2 - 1928*K1**2 + 2008*K1*K2*K3 + 24*K1*K3*K4 - 24*K2**4 + 40*K2**2*K4 - 2528*K2**2 - 384*K3**2 - 18*K4**2 + 2528 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {5}, {1, 4}, {3}], [{3, 6}, {2, 5}, {1, 4}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}], [{6}, {2, 5}, {1, 4}, {3}]] |
| If K is slice | False |