| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,0,1,3,3,1,2,1,1,1,0,0,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1018'] |
| Arrow polynomial of the knot is: 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.206', '6.236', '6.575', '6.580', '6.613', '6.619', '6.810', '6.819', '6.831', '6.838', '6.957', '6.1018', '6.1028', '6.1046', '6.1073', '6.1279', '6.1507', '6.1532', '6.1556', '6.1639', '6.1688', '6.1924', '6.1931'] |
| Outer characteristic polynomial of the knot is: t^7+31t^5+63t^3+10t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1018'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 224*K1**4*K2 - 1104*K1**4 + 96*K1**3*K2*K3 - 32*K1**3*K3 - 256*K1**2*K2**4 + 672*K1**2*K2**3 - 3872*K1**2*K2**2 - 32*K1**2*K2*K4 + 5344*K1**2*K2 - 48*K1**2*K3**2 - 3564*K1**2 + 640*K1*K2**3*K3 - 512*K1*K2**2*K3 - 128*K1*K2**2*K5 + 3720*K1*K2*K3 + 112*K1*K3*K4 + 8*K1*K4*K5 - 192*K2**6 + 128*K2**4*K4 - 1344*K2**4 - 336*K2**2*K3**2 - 16*K2**2*K4**2 + 1032*K2**2*K4 - 2096*K2**2 + 104*K2*K3*K5 - 968*K3**2 - 184*K4**2 - 4*K5**2 + 2670 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1018'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11282', 'vk6.11360', 'vk6.12547', 'vk6.12658', 'vk6.18365', 'vk6.18705', 'vk6.24815', 'vk6.25274', 'vk6.30964', 'vk6.31089', 'vk6.32146', 'vk6.32265', 'vk6.36993', 'vk6.37445', 'vk6.44175', 'vk6.44496', 'vk6.52034', 'vk6.52121', 'vk6.52881', 'vk6.52946', 'vk6.56137', 'vk6.56365', 'vk6.60660', 'vk6.61007', 'vk6.63655', 'vk6.63700', 'vk6.64087', 'vk6.64132', 'vk6.65791', 'vk6.66049', 'vk6.68793', 'vk6.69003'] |
| 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 | O1O2O3O4U3U1O5U4O6U5U2U6 |
| R3 orbit | {'O1O2O3O4U3U1O5U4O6U5U2U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U3U6O5U1O6U4U2 |
| Gauss code of K* | O1O2O3U4U2U5U6O5O4U1O6U3 |
| Gauss code of -K* | O1O2O3U1O4U3O5O6U4U6U2U5 |
| 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 -1 1 0 2],[ 2 0 2 0 2 1 1],[ 0 -2 0 -1 0 1 2],[ 1 0 1 0 1 1 0],[-1 -2 0 -1 0 1 1],[ 0 -1 -1 -1 -1 0 1],[-2 -1 -2 0 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 -1 -2 0 -1],[-1 1 0 1 0 -1 -2],[ 0 1 -1 0 -1 -1 -1],[ 0 2 0 1 0 -1 -2],[ 1 0 1 1 1 0 0],[ 2 1 2 1 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,1,2,0,1,-1,0,1,2,1,1,1,1,2,0] |
| Phi over symmetry | [-2,-1,0,0,1,2,0,0,1,3,3,1,2,1,1,1,0,0,0,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,1,0,1,1,3,0,0,1,3,-1,1,0,2,1,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,0,1,3,3,1,2,1,1,1,0,0,0,1,1] |
| Phi of -K* | [-2,-1,0,0,1,2,0,1,2,2,1,1,1,1,0,-1,-1,1,0,2,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 4z^2+23z+31 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2-2w^3z+25w^2z+31w |
| Inner characteristic polynomial | t^6+21t^4+17t^2+1 |
| Outer characteristic polynomial | t^7+31t^5+63t^3+10t |
| Flat arrow polynomial | 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 224*K1**4*K2 - 1104*K1**4 + 96*K1**3*K2*K3 - 32*K1**3*K3 - 256*K1**2*K2**4 + 672*K1**2*K2**3 - 3872*K1**2*K2**2 - 32*K1**2*K2*K4 + 5344*K1**2*K2 - 48*K1**2*K3**2 - 3564*K1**2 + 640*K1*K2**3*K3 - 512*K1*K2**2*K3 - 128*K1*K2**2*K5 + 3720*K1*K2*K3 + 112*K1*K3*K4 + 8*K1*K4*K5 - 192*K2**6 + 128*K2**4*K4 - 1344*K2**4 - 336*K2**2*K3**2 - 16*K2**2*K4**2 + 1032*K2**2*K4 - 2096*K2**2 + 104*K2*K3*K5 - 968*K3**2 - 184*K4**2 - 4*K5**2 + 2670 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}]] |
| If K is slice | False |