| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,1,2,0,2,0,0,1,0,1,-1,1,1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1556'] |
| 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+47t^5+256t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1556'] |
| 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 + 640*K1**2*K2**5 - 1984*K1**2*K2**4 - 128*K1**2*K2**3*K4 + 3648*K1**2*K2**3 + 192*K1**2*K2**2*K4 - 6832*K1**2*K2**2 - 352*K1**2*K2*K4 + 6112*K1**2*K2 - 32*K1**2*K3**2 - 3844*K1**2 + 1152*K1*K2**3*K3 - 1472*K1*K2**2*K3 - 192*K1*K2**2*K5 + 4504*K1*K2*K3 + 136*K1*K3*K4 + 8*K1*K4*K5 - 704*K2**6 + 288*K2**4*K4 - 2304*K2**4 - 192*K2**2*K3**2 - 16*K2**2*K4**2 + 1624*K2**2*K4 - 1360*K2**2 + 56*K2*K3*K5 - 872*K3**2 - 164*K4**2 - 4*K5**2 + 2634 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1556'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.10128', 'vk6.10177', 'vk6.10322', 'vk6.10417', 'vk6.17669', 'vk6.17716', 'vk6.24236', 'vk6.24282', 'vk6.29911', 'vk6.29950', 'vk6.30015', 'vk6.30072', 'vk6.36502', 'vk6.36600', 'vk6.43605', 'vk6.43711', 'vk6.51612', 'vk6.51641', 'vk6.51684', 'vk6.51715', 'vk6.55711', 'vk6.55768', 'vk6.60285', 'vk6.60341', 'vk6.63329', 'vk6.63344', 'vk6.63375', 'vk6.63394', 'vk6.65413', 'vk6.65454', 'vk6.68557', 'vk6.68585'] |
| 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 | O1O2O3U4O5U3U6O4O6U1U2U5 |
| R3 orbit | {'O1O2O3U4O5U3U6O4O6U1U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U2U3O5O6U5U1O4U6 |
| Gauss code of K* | O1O2O3U1U2U4O5U3O4O6U5U6 |
| Gauss code of -K* | O1O2O3U4U5O4O6U1O5U6U2U3 |
| 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 0 -1 2 1],[ 2 0 1 1 0 2 3],[ 0 -1 0 1 -2 1 1],[ 0 -1 -1 0 0 0 1],[ 1 0 2 0 0 3 1],[-2 -2 -1 0 -3 0 -2],[-1 -3 -1 -1 -1 2 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -2 0 -1 -3 -2],[-1 2 0 -1 -1 -1 -3],[ 0 0 1 0 -1 0 -1],[ 0 1 1 1 0 -2 -1],[ 1 3 1 0 2 0 0],[ 2 2 3 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,2,0,1,3,2,1,1,1,3,1,0,1,2,1,0] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,1,2,0,2,0,0,1,0,1,-1,1,1,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,1,1,1,0,2,-1,1,1,0,-1,0,1,0,2,-1] |
| Phi of K* | [-2,-1,0,0,1,2,-1,1,2,0,2,0,0,1,0,1,-1,1,1,1,1] |
| Phi of -K* | [-2,-1,0,0,1,2,0,1,1,3,2,0,2,1,3,-1,1,0,1,1,2] |
| 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+37t^4+188t^2 |
| Outer characteristic polynomial | t^7+47t^5+256t^3+8t |
| 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 + 640*K1**2*K2**5 - 1984*K1**2*K2**4 - 128*K1**2*K2**3*K4 + 3648*K1**2*K2**3 + 192*K1**2*K2**2*K4 - 6832*K1**2*K2**2 - 352*K1**2*K2*K4 + 6112*K1**2*K2 - 32*K1**2*K3**2 - 3844*K1**2 + 1152*K1*K2**3*K3 - 1472*K1*K2**2*K3 - 192*K1*K2**2*K5 + 4504*K1*K2*K3 + 136*K1*K3*K4 + 8*K1*K4*K5 - 704*K2**6 + 288*K2**4*K4 - 2304*K2**4 - 192*K2**2*K3**2 - 16*K2**2*K4**2 + 1624*K2**2*K4 - 1360*K2**2 + 56*K2*K3*K5 - 872*K3**2 - 164*K4**2 - 4*K5**2 + 2634 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {1, 5}, {2, 3}]] |
| If K is slice | False |