| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,0,1,2,2,-1,1,0,0,-1,-1,0,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1971'] |
| 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+27t^5+84t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1971'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 608*K1**4*K2 - 2768*K1**4 - 864*K1**3*K3 - 1504*K1**2*K2**2 + 6360*K1**2*K2 - 48*K1**2*K3**2 - 3780*K1**2 + 2888*K1*K2*K3 + 144*K1*K3*K4 - 24*K2**4 + 72*K2**2*K4 - 2848*K2**2 - 972*K3**2 - 90*K4**2 + 2888 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1971'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16574', 'vk6.16665', 'vk6.18135', 'vk6.18469', 'vk6.22973', 'vk6.23092', 'vk6.24590', 'vk6.25001', 'vk6.34966', 'vk6.35085', 'vk6.36733', 'vk6.37150', 'vk6.42535', 'vk6.42644', 'vk6.44001', 'vk6.44311', 'vk6.54821', 'vk6.54899', 'vk6.55937', 'vk6.56231', 'vk6.59249', 'vk6.59321', 'vk6.60472', 'vk6.60831', 'vk6.64795', 'vk6.64858', 'vk6.65598', 'vk6.65903', 'vk6.68093', 'vk6.68156', 'vk6.68669', 'vk6.68878'] |
| 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 | O1O2U3O4O5U4U6O3U1O6U2U5 |
| R3 orbit | {'O1O2U3O4O5U4U6O3U1O6U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2U3O4O5U1U4O6U5O3U6U2 |
| Gauss code of K* | O1O2U3O4U2O5O6U4U5O3U1U6 |
| Gauss code of -K* | O1O2U3O4U5O3O6U1U6O5U2U4 |
| 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 0 0 -1 2 0],[ 1 0 0 1 0 1 2],[ 0 0 0 -1 0 1 1],[ 0 -1 1 0 -1 2 -1],[ 1 0 0 1 0 1 1],[-2 -1 -1 -2 -1 0 -2],[ 0 -2 -1 1 -1 2 0]] |
| Primitive based matrix | [[ 0 2 0 0 0 -1 -1],[-2 0 -1 -2 -2 -1 -1],[ 0 1 0 1 -1 0 0],[ 0 2 -1 0 1 -1 -2],[ 0 2 1 -1 0 -1 -1],[ 1 1 0 1 1 0 0],[ 1 1 0 2 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,0,0,0,1,1,1,2,2,1,1,-1,1,0,0,-1,1,2,1,1,0] |
| Phi over symmetry | [-2,0,0,0,1,1,0,0,1,2,2,-1,1,0,0,-1,-1,0,1,1,0] |
| Phi of -K | [-1,-1,0,0,0,2,0,-1,0,1,2,0,0,1,2,-1,1,0,-1,0,1] |
| Phi of K* | [-2,0,0,0,1,1,0,0,1,2,2,-1,1,0,0,-1,-1,0,1,1,0] |
| Phi of -K* | [-1,-1,0,0,0,2,0,0,1,1,1,0,1,2,1,-1,1,1,-1,2,2] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | z^2+18z+33 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+18w^2z+33w |
| Inner characteristic polynomial | t^6+21t^4+59t^2+4 |
| Outer characteristic polynomial | t^7+27t^5+84t^3+8t |
| Flat arrow polynomial | -6*K1**2 + 3*K2 + 4 |
| 2-strand cable arrow polynomial | -64*K1**6 + 608*K1**4*K2 - 2768*K1**4 - 864*K1**3*K3 - 1504*K1**2*K2**2 + 6360*K1**2*K2 - 48*K1**2*K3**2 - 3780*K1**2 + 2888*K1*K2*K3 + 144*K1*K3*K4 - 24*K2**4 + 72*K2**2*K4 - 2848*K2**2 - 972*K3**2 - 90*K4**2 + 2888 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{2, 6}, {5}, {1, 4}, {3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |