| Min(phi) over symmetries of the knot is: [-1,-1,0,0,1,1,-1,0,1,1,1,0,1,0,1,-1,1,0,0,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1996'] |
| Arrow polynomial of the knot is: -12*K1**2 + 6*K2 + 7 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.612', '6.1246', '6.1402', '6.1410', '6.1411', '6.1468', '6.1617', '6.1666', '6.1667', '6.1815', '6.1904', '6.1994', '6.1995', '6.1996', '6.2001', '6.2014', '6.2015', '6.2016', '6.2017', '6.2020', '6.2022'] |
| Outer characteristic polynomial of the knot is: t^7+14t^5+30t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1996', '6.2083'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**6 - 320*K1**4*K2**2 + 1632*K1**4*K2 - 4352*K1**4 + 576*K1**3*K2*K3 - 736*K1**3*K3 - 4608*K1**2*K2**2 - 128*K1**2*K2*K4 + 8160*K1**2*K2 - 288*K1**2*K3**2 - 2916*K1**2 + 4160*K1*K2*K3 + 232*K1*K3*K4 - 176*K2**4 + 152*K2**2*K4 - 2832*K2**2 - 964*K3**2 - 96*K4**2 + 2950 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1996'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4121', 'vk6.4154', 'vk6.5359', 'vk6.5392', 'vk6.7489', 'vk6.7520', 'vk6.8990', 'vk6.9023', 'vk6.12439', 'vk6.12470', 'vk6.13343', 'vk6.13566', 'vk6.13599', 'vk6.14255', 'vk6.14702', 'vk6.14743', 'vk6.15199', 'vk6.15858', 'vk6.15897', 'vk6.30844', 'vk6.30875', 'vk6.32028', 'vk6.32059', 'vk6.33067', 'vk6.33100', 'vk6.33854', 'vk6.34317', 'vk6.48483', 'vk6.50268', 'vk6.53515', 'vk6.53943', 'vk6.54274'] |
| 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 | O1O2U1O3U2O4U5U3O5O6U4U6 |
| R3 orbit | {'O1O2U1O3U2O4U5U3O5O6U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2U3U4O3O5U6U5O4U1O6U2 |
| Gauss code of K* | O1O2U1U3O4O3U5U6O5U2O6U4 |
| Gauss code of -K* | O1O2U3O4U1O5U4U5O6O3U6U2 |
| 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 -1 0 1 0 -1 1],[ 1 0 1 1 0 1 0],[ 0 -1 0 1 1 -1 0],[-1 -1 -1 0 0 -1 1],[ 0 0 -1 0 0 0 1],[ 1 -1 1 1 0 0 1],[-1 0 0 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 -1 -1],[-1 0 1 0 -1 -1 -1],[-1 -1 0 -1 0 0 -1],[ 0 0 1 0 -1 0 0],[ 0 1 0 1 0 -1 -1],[ 1 1 0 0 1 0 1],[ 1 1 1 0 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,1,1,-1,0,1,1,1,1,0,0,1,1,0,0,1,1,-1] |
| Phi over symmetry | [-1,-1,0,0,1,1,-1,0,1,1,1,0,1,0,1,-1,1,0,0,1,-1] |
| Phi of -K | [-1,-1,0,0,1,1,-1,0,1,1,2,0,1,1,1,-1,0,1,1,0,-1] |
| Phi of K* | [-1,-1,0,0,1,1,-1,0,1,1,2,1,0,1,1,-1,1,1,0,0,-1] |
| Phi of -K* | [-1,-1,0,0,1,1,-1,0,1,1,1,0,1,0,1,-1,1,0,0,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+10t^4+18t^2+1 |
| Outer characteristic polynomial | t^7+14t^5+30t^3+5t |
| Flat arrow polynomial | -12*K1**2 + 6*K2 + 7 |
| 2-strand cable arrow polynomial | -448*K1**6 - 320*K1**4*K2**2 + 1632*K1**4*K2 - 4352*K1**4 + 576*K1**3*K2*K3 - 736*K1**3*K3 - 4608*K1**2*K2**2 - 128*K1**2*K2*K4 + 8160*K1**2*K2 - 288*K1**2*K3**2 - 2916*K1**2 + 4160*K1*K2*K3 + 232*K1*K3*K4 - 176*K2**4 + 152*K2**2*K4 - 2832*K2**2 - 964*K3**2 - 96*K4**2 + 2950 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}]] |
| If K is slice | True |