| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,0,1,1,2,1,1,1,2,2,0,1,1,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1379'] |
| 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+35t^5+31t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1379'] |
| 2-strand cable arrow polynomial of the knot is: 608*K1**4*K2 - 3344*K1**4 - 704*K1**3*K3 + 544*K1**2*K2**3 - 4736*K1**2*K2**2 - 480*K1**2*K2*K4 + 9336*K1**2*K2 - 496*K1**2*K3**2 - 5384*K1**2 - 32*K1*K2**2*K3 + 5528*K1*K2*K3 + 560*K1*K3*K4 - 568*K2**4 + 528*K2**2*K4 - 3856*K2**2 - 1400*K3**2 - 218*K4**2 + 4112 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1379'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73355', 'vk6.73384', 'vk6.73516', 'vk6.73562', 'vk6.73713', 'vk6.73830', 'vk6.74264', 'vk6.74889', 'vk6.75321', 'vk6.75525', 'vk6.75834', 'vk6.76437', 'vk6.78239', 'vk6.78309', 'vk6.78484', 'vk6.78625', 'vk6.78818', 'vk6.79316', 'vk6.80062', 'vk6.80091', 'vk6.80210', 'vk6.80259', 'vk6.80395', 'vk6.80777', 'vk6.81957', 'vk6.82684', 'vk6.84756', 'vk6.85052', 'vk6.85166', 'vk6.86520', 'vk6.87338', 'vk6.89431'] |
| 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 | O1O2O3U4O5O6U2U5U1O4U6U3 |
| R3 orbit | {'O1O2O3U4O5O6U2U5U1O4U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U4O5U3U6U2O4O6U5 |
| Gauss code of K* | O1O2O3U4O5O6U3U1U6O4U2U5 |
| Gauss code of -K* | O1O2O3U4U2O5U6U3U1O6O4U5 |
| 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 -2 2 -1 0 2],[ 1 0 -1 2 0 1 2],[ 2 1 0 2 1 1 1],[-2 -2 -2 0 -1 -1 0],[ 1 0 -1 1 0 0 1],[ 0 -1 -1 1 0 0 1],[-2 -2 -1 0 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 2 0 -1 -1 -2],[-2 0 0 -1 -1 -2 -1],[-2 0 0 -1 -1 -2 -2],[ 0 1 1 0 0 -1 -1],[ 1 1 1 0 0 0 -1],[ 1 2 2 1 0 0 -1],[ 2 1 2 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,1,1,2,0,1,1,2,1,1,1,2,2,0,1,1,0,1,1] |
| Phi over symmetry | [-2,-2,0,1,1,2,0,1,1,2,1,1,1,2,2,0,1,1,0,1,1] |
| Phi of -K | [-2,-1,-1,0,2,2,0,0,1,2,3,0,0,1,1,1,2,2,1,1,0] |
| Phi of K* | [-2,-2,0,1,1,2,0,1,1,2,2,1,1,2,3,0,1,1,0,0,0] |
| Phi of -K* | [-2,-1,-1,0,2,2,1,1,1,1,2,0,0,1,1,1,2,2,1,1,0] |
| 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^6+21t^4+12t^2+1 |
| Outer characteristic polynomial | t^7+35t^5+31t^3+5t |
| Flat arrow polynomial | -6*K1**2 + 3*K2 + 4 |
| 2-strand cable arrow polynomial | 608*K1**4*K2 - 3344*K1**4 - 704*K1**3*K3 + 544*K1**2*K2**3 - 4736*K1**2*K2**2 - 480*K1**2*K2*K4 + 9336*K1**2*K2 - 496*K1**2*K3**2 - 5384*K1**2 - 32*K1*K2**2*K3 + 5528*K1*K2*K3 + 560*K1*K3*K4 - 568*K2**4 + 528*K2**2*K4 - 3856*K2**2 - 1400*K3**2 - 218*K4**2 + 4112 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {5}, {4}, {2, 3}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {5}, {2, 3}, {1}], [{5, 6}, {1, 4}, {2, 3}], [{6}, {5}, {1, 4}, {2, 3}]] |
| If K is slice | False |