| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,0,1,1,1,2,1,1,1,3,0,1,1,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1466'] |
| 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+47t^5+47t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1466'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 768*K1**4*K2 - 4880*K1**4 + 480*K1**3*K2*K3 - 896*K1**3*K3 - 3776*K1**2*K2**2 - 160*K1**2*K2*K4 + 9528*K1**2*K2 - 208*K1**2*K3**2 - 4048*K1**2 - 96*K1*K2**2*K3 + 4504*K1*K2*K3 + 160*K1*K3*K4 - 56*K2**4 + 128*K2**2*K4 - 3656*K2**2 - 1184*K3**2 - 62*K4**2 + 3644 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1466'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17112', 'vk6.17353', 'vk6.20574', 'vk6.21981', 'vk6.23503', 'vk6.23840', 'vk6.28036', 'vk6.29493', 'vk6.35656', 'vk6.36091', 'vk6.39442', 'vk6.41641', 'vk6.43016', 'vk6.43326', 'vk6.46026', 'vk6.47692', 'vk6.55251', 'vk6.55501', 'vk6.57456', 'vk6.58621', 'vk6.59653', 'vk6.59999', 'vk6.62127', 'vk6.63091', 'vk6.65057', 'vk6.65250', 'vk6.66984', 'vk6.67847', 'vk6.68318', 'vk6.68466', 'vk6.69599', 'vk6.70290'] |
| 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 | O1O2O3U1O4U3O5U2U6U4O6U5 |
| R3 orbit | {'O1O2O3U1O4U3O5U2U6U4O6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4O5U6U5U2O4U1O6U3 |
| Gauss code of K* | O1O2O3U2O4U5U1U6O5U3O6U4 |
| Gauss code of -K* | O1O2O3U4O5U1O6U5U3U6O4U2 |
| 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 -1 0 2 2 -1],[ 2 0 2 1 2 1 2],[ 1 -2 0 0 2 2 0],[ 0 -1 0 0 1 1 -1],[-2 -2 -2 -1 0 0 -2],[-2 -1 -2 -1 0 0 -2],[ 1 -2 0 1 2 2 0]] |
| Primitive based matrix | [[ 0 2 2 0 -1 -1 -2],[-2 0 0 -1 -2 -2 -1],[-2 0 0 -1 -2 -2 -2],[ 0 1 1 0 0 -1 -1],[ 1 2 2 0 0 0 -2],[ 1 2 2 1 0 0 -2],[ 2 1 2 1 2 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,1,1,2,0,1,2,2,1,1,2,2,2,0,1,1,0,2,2] |
| Phi over symmetry | [-2,-2,0,1,1,2,0,1,1,1,2,1,1,1,3,0,1,1,0,-1,-1] |
| Phi of -K | [-2,-1,-1,0,2,2,-1,-1,1,2,3,0,0,1,1,1,1,1,1,1,0] |
| Phi of K* | [-2,-2,0,1,1,2,0,1,1,1,2,1,1,1,3,0,1,1,0,-1,-1] |
| Phi of -K* | [-2,-1,-1,0,2,2,2,2,1,1,2,0,0,2,2,1,2,2,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 2z^2+23z+39 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+23w^2z+39w |
| Inner characteristic polynomial | t^6+33t^4+26t^2+4 |
| Outer characteristic polynomial | t^7+47t^5+47t^3+11t |
| Flat arrow polynomial | -6*K1**2 + 3*K2 + 4 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 768*K1**4*K2 - 4880*K1**4 + 480*K1**3*K2*K3 - 896*K1**3*K3 - 3776*K1**2*K2**2 - 160*K1**2*K2*K4 + 9528*K1**2*K2 - 208*K1**2*K3**2 - 4048*K1**2 - 96*K1*K2**2*K3 + 4504*K1*K2*K3 + 160*K1*K3*K4 - 56*K2**4 + 128*K2**2*K4 - 3656*K2**2 - 1184*K3**2 - 62*K4**2 + 3644 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |