| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,0,1,2,3,0,1,1,1,1,1,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1215', '7.43831'] |
| Arrow polynomial of the knot is: 12*K1**3 - 8*K1**2 - 8*K1*K2 - 5*K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.324', '6.672', '6.953', '6.1196', '6.1215', '6.1216', '6.1699'] |
| Outer characteristic polynomial of the knot is: t^7+35t^5+51t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1215', '7.43831'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 512*K1**4*K2 - 960*K1**4 + 96*K1**3*K2*K3 + 32*K1**3*K3*K4 - 128*K1**2*K2**4 + 544*K1**2*K2**3 - 2864*K1**2*K2**2 + 3008*K1**2*K2 - 128*K1**2*K3**2 - 112*K1**2*K4**2 - 2008*K1**2 + 352*K1*K2**3*K3 + 2392*K1*K2*K3 + 432*K1*K3*K4 + 88*K1*K4*K5 + 8*K1*K5*K6 - 224*K2**6 + 192*K2**4*K4 - 1328*K2**4 - 464*K2**2*K3**2 - 128*K2**2*K4**2 + 976*K2**2*K4 - 1030*K2**2 + 240*K2*K3*K5 + 72*K2*K4*K6 - 784*K3**2 - 420*K4**2 - 64*K5**2 - 18*K6**2 + 1906 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1215'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11296', 'vk6.11374', 'vk6.12557', 'vk6.12668', 'vk6.18355', 'vk6.18694', 'vk6.24797', 'vk6.25256', 'vk6.30980', 'vk6.31107', 'vk6.32160', 'vk6.32279', 'vk6.36979', 'vk6.37434', 'vk6.44162', 'vk6.44483', 'vk6.52052', 'vk6.52135', 'vk6.52891', 'vk6.52954', 'vk6.56129', 'vk6.56354', 'vk6.60646', 'vk6.60989', 'vk6.63669', 'vk6.63714', 'vk6.64097', 'vk6.64142', 'vk6.65779', 'vk6.66039', 'vk6.68781', 'vk6.68990'] |
| 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 | O1O2O3O4U2U5U4O6O5U3U1U6 |
| R3 orbit | {'O1O2O3O4U2U5U4O6O5U3U1U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U4U2O6O5U1U6U3 |
| Gauss code of K* | O1O2O3U4U2O5O6O4U6U1U5U3 |
| Gauss code of -K* | O1O2O3U4U1O5O4O6U5U3U6U2 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -1 -2 0 2 0 1],[ 1 0 -2 1 2 0 1],[ 2 2 0 2 1 1 1],[ 0 -1 -2 0 1 -1 0],[-2 -2 -1 -1 0 -2 -1],[ 0 0 -1 1 2 0 1],[-1 -1 -1 0 1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 -1 -2 -2 -1],[-1 1 0 0 -1 -1 -1],[ 0 1 0 0 -1 -1 -2],[ 0 2 1 1 0 0 -1],[ 1 2 1 1 0 0 -2],[ 2 1 1 2 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,1,2,2,1,0,1,1,1,1,1,2,0,1,2] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,0,1,2,3,0,1,1,1,1,1,1,0,0,0] |
| Phi of -K | [-2,-1,0,0,1,2,-1,0,1,2,3,0,1,1,1,1,1,1,0,0,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,0,1,1,3,0,1,1,2,1,1,1,0,0,-1] |
| Phi of -K* | [-2,-1,0,0,1,2,2,1,2,1,1,0,1,1,2,1,1,2,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 9z+19 |
| Enhanced Jones-Krushkal polynomial | -6w^3z+15w^2z+19w |
| Inner characteristic polynomial | t^6+25t^4+15t^2 |
| Outer characteristic polynomial | t^7+35t^5+51t^3 |
| Flat arrow polynomial | 12*K1**3 - 8*K1**2 - 8*K1*K2 - 5*K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 512*K1**4*K2 - 960*K1**4 + 96*K1**3*K2*K3 + 32*K1**3*K3*K4 - 128*K1**2*K2**4 + 544*K1**2*K2**3 - 2864*K1**2*K2**2 + 3008*K1**2*K2 - 128*K1**2*K3**2 - 112*K1**2*K4**2 - 2008*K1**2 + 352*K1*K2**3*K3 + 2392*K1*K2*K3 + 432*K1*K3*K4 + 88*K1*K4*K5 + 8*K1*K5*K6 - 224*K2**6 + 192*K2**4*K4 - 1328*K2**4 - 464*K2**2*K3**2 - 128*K2**2*K4**2 + 976*K2**2*K4 - 1030*K2**2 + 240*K2*K3*K5 + 72*K2*K4*K6 - 784*K3**2 - 420*K4**2 - 64*K5**2 - 18*K6**2 + 1906 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}]] |
| If K is slice | True |