| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,1,1,2,2,1,1,1,0,-1,0,0,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1073'] |
| 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+27t^5+48t^3+12t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1073'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 320*K1**4*K2 - 768*K1**4 + 160*K1**3*K2*K3 - 64*K1**3*K3 + 384*K1**2*K2**5 - 1728*K1**2*K2**4 + 2976*K1**2*K2**3 + 192*K1**2*K2**2*K4 - 6432*K1**2*K2**2 - 544*K1**2*K2*K4 + 5568*K1**2*K2 - 32*K1**2*K3**2 - 3412*K1**2 - 384*K1*K2**4*K3 + 1728*K1*K2**3*K3 + 96*K1*K2**2*K3*K4 - 672*K1*K2**2*K3 - 64*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 3912*K1*K2*K3 + 320*K1*K3*K4 - 448*K2**6 + 448*K2**4*K4 - 1968*K2**4 - 560*K2**2*K3**2 - 112*K2**2*K4**2 + 1008*K2**2*K4 - 1032*K2**2 + 104*K2*K3*K5 - 748*K3**2 - 232*K4**2 + 2334 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1073'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.10135', 'vk6.10190', 'vk6.10333', 'vk6.10422', 'vk6.17666', 'vk6.17715', 'vk6.24229', 'vk6.24278', 'vk6.29914', 'vk6.29955', 'vk6.30018', 'vk6.30073', 'vk6.36497', 'vk6.36593', 'vk6.43590', 'vk6.43702', 'vk6.51623', 'vk6.51662', 'vk6.51711', 'vk6.51728', 'vk6.55696', 'vk6.55755', 'vk6.60262', 'vk6.60326', 'vk6.63336', 'vk6.63365', 'vk6.63385', 'vk6.63403', 'vk6.65406', 'vk6.65447', 'vk6.68542', 'vk6.68575'] |
| 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 | O1O2O3O4U5U4O6U1O5U6U2U3 |
| R3 orbit | {'O1O2O3O4U5U4O6U1O5U6U2U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U3U5O6U4O5U1U6 |
| Gauss code of K* | O1O2O3U4U2U3U5O6O5U1O4U6 |
| Gauss code of -K* | O1O2O3U4O5U3O6O4U6U1U2U5 |
| 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 2 1 -1 0],[ 2 0 1 2 0 1 0],[ 0 -1 0 1 1 0 -1],[-2 -2 -1 0 1 -2 -1],[-1 0 -1 -1 0 -1 -1],[ 1 -1 0 2 1 0 0],[ 0 0 1 1 1 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 1 -1 -1 -2 -2],[-1 -1 0 -1 -1 -1 0],[ 0 1 1 0 1 0 0],[ 0 1 1 -1 0 0 -1],[ 1 2 1 0 0 0 -1],[ 2 2 0 0 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,-1,1,1,2,2,1,1,1,0,-1,0,0,0,1,1] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,1,1,2,2,1,1,1,0,-1,0,0,0,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,0,1,2,3,2,1,1,1,1,1,0,1,0,1,2] |
| Phi of K* | [-2,-1,0,0,1,2,2,1,1,1,2,0,0,1,3,-1,1,1,1,2,0] |
| Phi of -K* | [-2,-1,0,0,1,2,1,0,1,0,2,0,0,1,2,1,1,1,1,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 5z^2+22z+25 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+7w^3z^2-2w^3z+24w^2z+25w |
| Inner characteristic polynomial | t^6+17t^4+20t^2+4 |
| Outer characteristic polynomial | t^7+27t^5+48t^3+12t |
| Flat arrow polynomial | 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 320*K1**4*K2 - 768*K1**4 + 160*K1**3*K2*K3 - 64*K1**3*K3 + 384*K1**2*K2**5 - 1728*K1**2*K2**4 + 2976*K1**2*K2**3 + 192*K1**2*K2**2*K4 - 6432*K1**2*K2**2 - 544*K1**2*K2*K4 + 5568*K1**2*K2 - 32*K1**2*K3**2 - 3412*K1**2 - 384*K1*K2**4*K3 + 1728*K1*K2**3*K3 + 96*K1*K2**2*K3*K4 - 672*K1*K2**2*K3 - 64*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 3912*K1*K2*K3 + 320*K1*K3*K4 - 448*K2**6 + 448*K2**4*K4 - 1968*K2**4 - 560*K2**2*K3**2 - 112*K2**2*K4**2 + 1008*K2**2*K4 - 1032*K2**2 + 104*K2*K3*K5 - 748*K3**2 - 232*K4**2 + 2334 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}]] |
| If K is slice | False |