| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,0,1,2,3,0,0,1,1,0,1,1,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1532'] |
| 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+35t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1532'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**4*K2**2 + 256*K1**4*K2 - 944*K1**4 + 352*K1**3*K2*K3 - 224*K1**3*K3 + 448*K1**2*K2**3 - 3520*K1**2*K2**2 - 224*K1**2*K2*K4 + 4408*K1**2*K2 - 240*K1**2*K3**2 - 3044*K1**2 + 512*K1*K2**3*K3 - 448*K1*K2**2*K3 - 64*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4032*K1*K2*K3 + 368*K1*K3*K4 + 8*K1*K4*K5 - 64*K2**6 + 128*K2**4*K4 - 1024*K2**4 - 496*K2**2*K3**2 - 48*K2**2*K4**2 + 928*K2**2*K4 - 2120*K2**2 + 296*K2*K3*K5 - 1200*K3**2 - 300*K4**2 - 52*K5**2 + 2498 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1532'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11278', 'vk6.11356', 'vk6.12543', 'vk6.12654', 'vk6.18362', 'vk6.18701', 'vk6.24812', 'vk6.25269', 'vk6.30954', 'vk6.31077', 'vk6.32134', 'vk6.32253', 'vk6.36998', 'vk6.37447', 'vk6.44179', 'vk6.44499', 'vk6.52046', 'vk6.52129', 'vk6.52889', 'vk6.52952', 'vk6.56135', 'vk6.56361', 'vk6.60657', 'vk6.61002', 'vk6.63659', 'vk6.63704', 'vk6.64091', 'vk6.64136', 'vk6.65796', 'vk6.66051', 'vk6.68797', 'vk6.69006'] |
| 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 | O1O2O3U2O4U5U3O6O5U1U6U4 |
| R3 orbit | {'O1O2O3U2O4U5U3O6O5U1U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U3O6O5U1U6O4U2 |
| Gauss code of K* | O1O2O3U1U4U5O4U3O6O5U2U6 |
| Gauss code of -K* | O1O2O3U4U2O5O4U1O6U5U6U3 |
| 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 1 2 0 0],[ 2 0 -1 2 3 1 0],[ 1 1 0 1 1 0 0],[-1 -2 -1 0 0 -1 -1],[-2 -3 -1 0 0 -1 -1],[ 0 -1 0 1 1 0 0],[ 0 0 0 1 1 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 0 -1 -1 -1 -3],[-1 0 0 -1 -1 -1 -2],[ 0 1 1 0 0 0 0],[ 0 1 1 0 0 0 -1],[ 1 1 1 0 0 0 1],[ 2 3 2 0 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,0,1,1,1,3,1,1,1,2,0,0,0,0,1,-1] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,0,1,2,3,0,0,1,1,0,1,1,1,1,0] |
| Phi of -K | [-2,-1,0,0,1,2,2,1,2,1,1,1,1,1,2,0,0,1,0,1,1] |
| Phi of K* | [-2,-1,0,0,1,2,1,1,1,2,1,0,0,1,1,0,1,1,1,2,2] |
| Phi of -K* | [-2,-1,0,0,1,2,-1,0,1,2,3,0,0,1,1,0,1,1,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 3z^2+20z+29 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+20w^2z+29w |
| Inner characteristic polynomial | t^6+21t^4+15t^2 |
| Outer characteristic polynomial | t^7+31t^5+35t^3+4t |
| Flat arrow polynomial | 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| 2-strand cable arrow polynomial | -128*K1**4*K2**2 + 256*K1**4*K2 - 944*K1**4 + 352*K1**3*K2*K3 - 224*K1**3*K3 + 448*K1**2*K2**3 - 3520*K1**2*K2**2 - 224*K1**2*K2*K4 + 4408*K1**2*K2 - 240*K1**2*K3**2 - 3044*K1**2 + 512*K1*K2**3*K3 - 448*K1*K2**2*K3 - 64*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4032*K1*K2*K3 + 368*K1*K3*K4 + 8*K1*K4*K5 - 64*K2**6 + 128*K2**4*K4 - 1024*K2**4 - 496*K2**2*K3**2 - 48*K2**2*K4**2 + 928*K2**2*K4 - 2120*K2**2 + 296*K2*K3*K5 - 1200*K3**2 - 300*K4**2 - 52*K5**2 + 2498 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |