| Min(phi) over symmetries of the knot is: [-2,0,0,1,1,0,1,1,3,0,-1,0,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1966', '7.39655'] |
| 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+21t^4+13t^2+1 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.84', '6.1966'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 1440*K1**4*K2 - 4144*K1**4 + 64*K1**3*K2*K3 - 448*K1**3*K3 + 96*K1**2*K2**3 - 3680*K1**2*K2**2 - 64*K1**2*K2*K4 + 8512*K1**2*K2 - 16*K1**2*K3**2 - 3880*K1**2 - 32*K1*K2**2*K3 + 2672*K1*K2*K3 + 24*K1*K3*K4 - 88*K2**4 + 72*K2**2*K4 - 3080*K2**2 - 480*K3**2 - 14*K4**2 + 3108 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1966'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71350', 'vk6.71402', 'vk6.71411', 'vk6.71861', 'vk6.71875', 'vk6.71924', 'vk6.71936', 'vk6.74325', 'vk6.74332', 'vk6.74972', 'vk6.74977', 'vk6.76537', 'vk6.76548', 'vk6.76945', 'vk6.77004', 'vk6.77006', 'vk6.77065', 'vk6.77066', 'vk6.77391', 'vk6.79378', 'vk6.79805', 'vk6.79808', 'vk6.80834', 'vk6.80843', 'vk6.81279', 'vk6.81479', 'vk6.81483', 'vk6.83840', 'vk6.87056', 'vk6.87086', 'vk6.88047', 'vk6.89559'] |
| 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 | O1O2U3O4O5U1U6O3U5O6U2U4 |
| R3 orbit | {'O1O2U3O4O5U1U6O3U5O6U2U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2U3O4O5U2U4O6U1O3U6U5 |
| Gauss code of K* | O1O2U3O4U2O5O6U1U5O3U6U4 |
| Gauss code of -K* | O1O2U3O4U5O3O6U4U1O5U2U6 |
| 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 -2 0 0 1 1 0],[ 2 0 1 2 2 0 2],[ 0 -1 0 0 0 0 0],[ 0 -2 0 0 1 1 0],[-1 -2 0 -1 0 1 -2],[-1 0 0 -1 -1 0 -1],[ 0 -2 0 0 2 1 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 -2],[-1 0 1 0 -2 -2],[-1 -1 0 0 -1 0],[ 0 0 0 0 0 -1],[ 0 2 1 0 0 -2],[ 2 2 0 1 2 0]] |
| If based matrix primitive | False |
| Phi of primitive based matrix | [-1,-1,0,0,2,-1,0,2,2,0,1,0,0,1,2] |
| Phi over symmetry | [-2,0,0,1,1,0,1,1,3,0,-1,0,1,1,-1] |
| Phi of -K | [-2,0,0,1,1,0,1,1,3,0,-1,0,1,1,-1] |
| Phi of K* | [-1,-1,0,0,2,-1,0,1,3,-1,1,1,0,0,1] |
| Phi of -K* | [-2,0,0,1,1,1,2,0,2,0,0,0,1,2,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 4z^2+25z+35 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+25w^2z+35w |
| Inner characteristic polynomial | t^5+15t^3+6t |
| Outer characteristic polynomial | t^6+21t^4+13t^2+1 |
| Flat arrow polynomial | -6*K1**2 + 3*K2 + 4 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 1440*K1**4*K2 - 4144*K1**4 + 64*K1**3*K2*K3 - 448*K1**3*K3 + 96*K1**2*K2**3 - 3680*K1**2*K2**2 - 64*K1**2*K2*K4 + 8512*K1**2*K2 - 16*K1**2*K3**2 - 3880*K1**2 - 32*K1*K2**2*K3 + 2672*K1*K2*K3 + 24*K1*K3*K4 - 88*K2**4 + 72*K2**2*K4 - 3080*K2**2 - 480*K3**2 - 14*K4**2 + 3108 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{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}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {5}, {3}, {1, 2}]] |
| If K is slice | False |