| Min(phi) over symmetries of the knot is: [-2,0,0,1,1,0,1,1,1,1,0,0,0,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1963', '7.34295', '7.38645'] |
| 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^6+11t^4+12t^2 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1963', '7.38645'] |
| 2-strand cable arrow polynomial of the knot is: -320*K1**6 - 192*K1**4*K2**2 + 672*K1**4*K2 - 2352*K1**4 + 128*K1**3*K2*K3 - 1184*K1**2*K2**2 + 3112*K1**2*K2 - 16*K1**2*K3**2 - 468*K1**2 + 760*K1*K2*K3 - 56*K2**4 + 40*K2**2*K4 - 920*K2**2 - 140*K3**2 - 6*K4**2 + 940 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1963'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16569', 'vk6.16662', 'vk6.18126', 'vk6.18462', 'vk6.22968', 'vk6.23089', 'vk6.24581', 'vk6.24994', 'vk6.34969', 'vk6.35090', 'vk6.36724', 'vk6.37143', 'vk6.42538', 'vk6.42649', 'vk6.43992', 'vk6.44304', 'vk6.54816', 'vk6.54896', 'vk6.55944', 'vk6.56240', 'vk6.59244', 'vk6.59319', 'vk6.60478', 'vk6.60840', 'vk6.64798', 'vk6.64863', 'vk6.65605', 'vk6.65912', 'vk6.68096', 'vk6.68161', 'vk6.68676', 'vk6.68887'] |
| 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 | O1O2U1O3O4U5U3O6U2O5U6U4 |
| R3 orbit | {'O1O2U1O3O4U5U3O6U2O5U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2U3O4O3U1U5O6U4O5U2U6 |
| Gauss code of K* | O1O2U3O4U1O3O5U6U4O6U2U5 |
| Gauss code of -K* | O1O2U3O4U2O5O3U1U5O6U4U6 |
| 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 0 0 2 -1 0],[ 1 0 1 0 1 0 1],[ 0 -1 0 0 2 -1 0],[ 0 0 0 0 0 0 -1],[-2 -1 -2 0 0 -1 -1],[ 1 0 1 0 1 0 0],[ 0 -1 0 1 1 0 0]] |
| Primitive based matrix | [[ 0 2 0 0 -1 -1],[-2 0 0 -1 -1 -1],[ 0 0 0 -1 0 0],[ 0 1 1 0 0 -1],[ 1 1 0 0 0 0],[ 1 1 0 1 0 0]] |
| If based matrix primitive | False |
| Phi of primitive based matrix | [-2,0,0,1,1,0,1,1,1,1,0,0,0,1,0] |
| Phi over symmetry | [-2,0,0,1,1,0,1,1,1,1,0,0,0,1,0] |
| Phi of -K | [-1,-1,0,0,2,0,0,1,2,1,1,2,-1,1,2] |
| Phi of K* | [-2,0,0,1,1,1,2,2,2,1,0,1,1,1,0] |
| Phi of -K* | [-1,-1,0,0,2,0,0,0,1,0,1,1,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 13z+27 |
| Enhanced Jones-Krushkal polynomial | 13w^2z+27w |
| Inner characteristic polynomial | t^5+5t^3+3t |
| Outer characteristic polynomial | t^6+11t^4+12t^2 |
| Flat arrow polynomial | -6*K1**2 + 3*K2 + 4 |
| 2-strand cable arrow polynomial | -320*K1**6 - 192*K1**4*K2**2 + 672*K1**4*K2 - 2352*K1**4 + 128*K1**3*K2*K3 - 1184*K1**2*K2**2 + 3112*K1**2*K2 - 16*K1**2*K3**2 - 468*K1**2 + 760*K1*K2*K3 - 56*K2**4 + 40*K2**2*K4 - 920*K2**2 - 140*K3**2 - 6*K4**2 + 940 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}], [{3, 6}, {5}, {1, 4}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {5}, {1, 3}, {2}], [{5, 6}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}]] |
| If K is slice | False |