| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,1,2,3,1,0,1,1,0,1,1,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.648'] |
| Arrow polynomial of the knot is: -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.323', '6.380', '6.444', '6.472', '6.523', '6.579', '6.592', '6.595', '6.609', '6.614', '6.620', '6.644', '6.648', '6.669', '6.671', '6.681', '6.693', '6.724', '6.725', '6.757', '6.766', '6.785', '6.786', '6.797', '6.798', '6.816', '6.833', '6.972', '6.978', '6.1056', '6.1064', '6.1066', '6.1087', '6.1094', '6.1273', '6.1277', '6.1282', '6.1295', '6.1300', '6.1313', '6.1344', '6.1353', '6.1354'] |
| Outer characteristic polynomial of the knot is: t^7+54t^5+39t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.648'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**6 - 128*K1**4*K2**2 + 768*K1**4*K2 - 1824*K1**4 + 128*K1**3*K2*K3 - 224*K1**3*K3 - 2208*K1**2*K2**2 - 32*K1**2*K2*K4 + 3616*K1**2*K2 - 160*K1**2*K3**2 - 1520*K1**2 - 192*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 2352*K1*K2*K3 + 320*K1*K3*K4 + 16*K1*K4*K5 - 168*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 368*K2**2*K4 - 1630*K2**2 + 112*K2*K3*K5 + 8*K2*K4*K6 - 708*K3**2 - 214*K4**2 - 44*K5**2 - 2*K6**2 + 1644 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.648'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11273', 'vk6.11353', 'vk6.12534', 'vk6.12647', 'vk6.17046', 'vk6.17289', 'vk6.17626', 'vk6.18908', 'vk6.18984', 'vk6.19351', 'vk6.19644', 'vk6.22256', 'vk6.24084', 'vk6.24178', 'vk6.25504', 'vk6.26123', 'vk6.26541', 'vk6.28316', 'vk6.30947', 'vk6.31072', 'vk6.31243', 'vk6.31594', 'vk6.32123', 'vk6.32244', 'vk6.32814', 'vk6.35553', 'vk6.36004', 'vk6.36429', 'vk6.37645', 'vk6.39944', 'vk6.40108', 'vk6.43528', 'vk6.44784', 'vk6.46490', 'vk6.52023', 'vk6.53390', 'vk6.55467', 'vk6.56649', 'vk6.65397', 'vk6.66117'] |
| 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 | O1O2O3O4U1O5U6U3O6U4U5U2 |
| R3 orbit | {'O1O2O3O4U1O5U4U6U3O6U5U2', 'O1O2O3O4U1O5U6U3O6U4U5U2'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U3U5U1O6U2U6O5U4 |
| Gauss code of K* | O1O2O3U4U3U5U1O4U2O6O5U6 |
| Gauss code of -K* | O1O2O3U4O5O4U2O6U3U5U1U6 |
| 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 -3 1 0 1 2 -1],[ 3 0 3 1 2 2 2],[-1 -3 0 -1 0 2 -2],[ 0 -1 1 0 0 1 0],[-1 -2 0 0 0 1 -1],[-2 -2 -2 -1 -1 0 -2],[ 1 -2 2 0 1 2 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 -1 -2 -1 -2 -2],[-1 1 0 0 0 -1 -2],[-1 2 0 0 -1 -2 -3],[ 0 1 0 1 0 0 -1],[ 1 2 1 2 0 0 -2],[ 3 2 2 3 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,1,2,1,2,2,0,0,1,2,1,2,3,0,1,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,1,2,3,1,0,1,1,0,1,1,0,-1,0] |
| Phi of -K | [-3,-1,0,1,1,2,0,2,1,2,3,1,0,1,1,0,1,1,0,-1,0] |
| Phi of K* | [-2,-1,-1,0,1,3,-1,0,1,1,3,0,0,0,1,1,1,2,1,2,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,1,2,3,2,0,1,2,2,0,1,1,0,1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | z^2+14z+25 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+14w^2z+25w |
| Inner characteristic polynomial | t^6+38t^4+16t^2+1 |
| Outer characteristic polynomial | t^7+54t^5+39t^3+4t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -192*K1**6 - 128*K1**4*K2**2 + 768*K1**4*K2 - 1824*K1**4 + 128*K1**3*K2*K3 - 224*K1**3*K3 - 2208*K1**2*K2**2 - 32*K1**2*K2*K4 + 3616*K1**2*K2 - 160*K1**2*K3**2 - 1520*K1**2 - 192*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 2352*K1*K2*K3 + 320*K1*K3*K4 + 16*K1*K4*K5 - 168*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 368*K2**2*K4 - 1630*K2**2 + 112*K2*K3*K5 + 8*K2*K4*K6 - 708*K3**2 - 214*K4**2 - 44*K5**2 - 2*K6**2 + 1644 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {2, 5}, {1, 4}]] |
| If K is slice | False |