| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,2,2,2,1,1,1,1,0,1,-1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1126'] |
| 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+28t^5+60t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1126'] |
| 2-strand cable arrow polynomial of the knot is: 128*K1**4*K2 - 1792*K1**4 + 32*K1**3*K2*K3 - 64*K1**3*K3 - 1360*K1**2*K2**2 - 32*K1**2*K2*K4 + 3280*K1**2*K2 - 32*K1**2*K3**2 - 1244*K1**2 - 96*K1*K2**2*K3 + 1504*K1*K2*K3 + 88*K1*K3*K4 - 88*K2**4 + 136*K2**2*K4 - 1272*K2**2 - 412*K3**2 - 54*K4**2 + 1276 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1126'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4349', 'vk6.4382', 'vk6.5667', 'vk6.5700', 'vk6.7732', 'vk6.7765', 'vk6.9210', 'vk6.9243', 'vk6.10493', 'vk6.10543', 'vk6.10638', 'vk6.10714', 'vk6.10747', 'vk6.10825', 'vk6.14616', 'vk6.15299', 'vk6.15424', 'vk6.16239', 'vk6.17990', 'vk6.24430', 'vk6.24672', 'vk6.30172', 'vk6.30222', 'vk6.30317', 'vk6.30444', 'vk6.30582', 'vk6.30677', 'vk6.33941', 'vk6.34346', 'vk6.34401', 'vk6.37250', 'vk6.43865', 'vk6.50435', 'vk6.50467', 'vk6.52672', 'vk6.52766', 'vk6.54219', 'vk6.60543', 'vk6.60883', 'vk6.65943'] |
| 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 | O1O2O3O4U3U5O6U4U1O5U2U6 |
| R3 orbit | {'O1O2O3U2O4U5U3O5U6U1O6U4', 'O1O2O3O4U3U5O6U4U1O5U2U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U5U3O6U4U1O5U6U2 |
| Gauss code of K* | O1O2U3O4O5U2O6O3U5U6U1U4 |
| Gauss code of -K* | O1O2U3O4O5U1O3O6U5U6U2U4 |
| 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 -1 1 -1 2],[ 1 0 0 -1 1 0 2],[ 0 0 0 -1 2 -1 1],[ 1 1 1 0 1 0 1],[-1 -1 -2 -1 0 -1 0],[ 1 0 1 0 1 0 2],[-2 -2 -1 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 0 -1 -1 -2 -2],[-1 0 0 -2 -1 -1 -1],[ 0 1 2 0 -1 0 -1],[ 1 1 1 1 0 1 0],[ 1 2 1 0 -1 0 0],[ 1 2 1 1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,0,1,1,2,2,2,1,1,1,1,0,1,-1,0,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,2,2,2,1,1,1,1,0,1,-1,0,0] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,0,1,2,0,1,1,1,0,1,1,-1,1,1] |
| Phi of K* | [-2,-1,0,1,1,1,1,1,1,1,2,-1,1,1,1,0,1,0,0,0,-1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,1,2,0,1,1,1,1,1,2,2,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 2z^2+15z+23 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+15w^2z+23w |
| Inner characteristic polynomial | t^6+20t^4+35t^2+4 |
| Outer characteristic polynomial | t^7+28t^5+60t^3+7t |
| Flat arrow polynomial | -6*K1**2 + 3*K2 + 4 |
| 2-strand cable arrow polynomial | 128*K1**4*K2 - 1792*K1**4 + 32*K1**3*K2*K3 - 64*K1**3*K3 - 1360*K1**2*K2**2 - 32*K1**2*K2*K4 + 3280*K1**2*K2 - 32*K1**2*K3**2 - 1244*K1**2 - 96*K1*K2**2*K3 + 1504*K1*K2*K3 + 88*K1*K3*K4 - 88*K2**4 + 136*K2**2*K4 - 1272*K2**2 - 412*K3**2 - 54*K4**2 + 1276 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {5}, {2, 4}, {3}]] |
| If K is slice | False |