| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,-1,1,1,2,2,1,1,0,2,1,0,1,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1828'] |
| Arrow polynomial of the knot is: -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.425', '6.655', '6.755', '6.769', '6.792', '6.1240', '6.1494', '6.1522', '6.1534', '6.1587', '6.1707', '6.1746', '6.1747', '6.1786', '6.1814', '6.1828', '6.1835', '6.1854', '6.1870'] |
| Outer characteristic polynomial of the knot is: t^7+26t^5+65t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1828'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**6 - 320*K1**4*K2**2 + 1472*K1**4*K2 - 4416*K1**4 + 1120*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1056*K1**3*K3 + 128*K1**2*K2**2*K4 - 4864*K1**2*K2**2 - 736*K1**2*K2*K4 + 9752*K1**2*K2 - 1312*K1**2*K3**2 - 208*K1**2*K4**2 - 6076*K1**2 - 768*K1*K2**2*K3 - 32*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 8312*K1*K2*K3 + 2200*K1*K3*K4 + 352*K1*K4*K5 + 24*K1*K5*K6 - 424*K2**4 - 480*K2**2*K3**2 - 112*K2**2*K4**2 + 1264*K2**2*K4 - 5476*K2**2 + 472*K2*K3*K5 + 136*K2*K4*K6 - 3024*K3**2 - 1126*K4**2 - 220*K5**2 - 52*K6**2 + 5788 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1828'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4245', 'vk6.4253', 'vk6.4325', 'vk6.4332', 'vk6.5522', 'vk6.5528', 'vk6.5641', 'vk6.5647', 'vk6.7715', 'vk6.7722', 'vk6.9117', 'vk6.9122', 'vk6.9197', 'vk6.9201', 'vk6.19827', 'vk6.19836', 'vk6.26260', 'vk6.26275', 'vk6.26705', 'vk6.26718', 'vk6.38210', 'vk6.38225', 'vk6.44983', 'vk6.45002', 'vk6.48555', 'vk6.48575', 'vk6.49264', 'vk6.49286', 'vk6.50407', 'vk6.50423', 'vk6.66364', 'vk6.66369'] |
| 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 | O1O2O3U1U3O4U5O6O5U2U6U4 |
| R3 orbit | {'O1O2O3U1U3O4U5O6O5U2U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U2O6O5U6O4U1U3 |
| Gauss code of K* | O1O2O3U4U1U5O4O5U3O6U2U6 |
| Gauss code of -K* | O1O2O3U4U2O4U1O5O6U5U3U6 |
| 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 1 1 0],[ 2 0 2 1 1 2 1],[ 1 -2 0 0 2 1 0],[-1 -1 0 0 0 -1 0],[-1 -1 -2 0 0 0 -1],[-1 -2 -1 1 0 0 0],[ 0 -1 0 0 1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 0 -1 -2],[-1 -1 0 0 0 0 -1],[-1 0 0 0 -1 -2 -1],[ 0 0 0 1 0 0 -1],[ 1 1 0 2 0 0 -2],[ 2 2 1 1 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,0,1,2,0,0,0,1,1,2,1,0,1,2] |
| Phi over symmetry | [-2,-1,0,1,1,1,-1,1,1,2,2,1,1,0,2,1,0,1,0,-1,0] |
| Phi of -K | [-2,-1,0,1,1,1,-1,1,1,2,2,1,1,0,2,1,0,1,0,-1,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,1,2,2,0,1,1,1,0,0,2,1,1,-1] |
| Phi of -K* | [-2,-1,0,1,1,1,2,1,1,1,2,0,0,2,1,0,1,0,0,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 2z^2+23z+39 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+23w^2z+39w |
| Inner characteristic polynomial | t^6+18t^4+36t^2+1 |
| Outer characteristic polynomial | t^7+26t^5+65t^3+4t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -192*K1**6 - 320*K1**4*K2**2 + 1472*K1**4*K2 - 4416*K1**4 + 1120*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1056*K1**3*K3 + 128*K1**2*K2**2*K4 - 4864*K1**2*K2**2 - 736*K1**2*K2*K4 + 9752*K1**2*K2 - 1312*K1**2*K3**2 - 208*K1**2*K4**2 - 6076*K1**2 - 768*K1*K2**2*K3 - 32*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 8312*K1*K2*K3 + 2200*K1*K3*K4 + 352*K1*K4*K5 + 24*K1*K5*K6 - 424*K2**4 - 480*K2**2*K3**2 - 112*K2**2*K4**2 + 1264*K2**2*K4 - 5476*K2**2 + 472*K2*K3*K5 + 136*K2*K4*K6 - 3024*K3**2 - 1126*K4**2 - 220*K5**2 - 52*K6**2 + 5788 |
| Genus of based matrix | 2 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{1, 6}, {5}, {2, 4}, {3}], [{1, 6}, {5}, {3, 4}, {2}], [{1, 6}, {5}, {4}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{2, 6}, {5}, {1, 4}, {3}], [{2, 6}, {5}, {3, 4}, {1}], [{2, 6}, {5}, {4}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}], [{3, 6}, {5}, {1, 4}, {2}], [{3, 6}, {5}, {2, 4}, {1}], [{3, 6}, {5}, {4}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{4, 6}, {5}, {1, 3}, {2}], [{4, 6}, {5}, {2, 3}, {1}], [{4, 6}, {5}, {3}, {1, 2}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}], [{5, 6}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}], [{5, 6}, {4}, {1, 3}, {2}], [{5, 6}, {4}, {2, 3}, {1}], [{5, 6}, {4}, {3}, {1, 2}], [{5, 6}, {4}, {3}, {2}, {1}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {3, 5}, {1, 4}, {2}], [{6}, {3, 5}, {2, 4}, {1}], [{6}, {3, 5}, {4}, {1, 2}], [{6}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {1, 4}, {3}, {2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {3}, {1, 2}]] |
| If K is slice | False |