| Min(phi) over symmetries of the knot is: [-4,-1,-1,2,2,2,1,2,2,3,4,0,0,1,1,1,2,1,0,-2,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.481'] |
| Arrow polynomial of the knot is: 4*K1**2*K2 - 2*K1*K3 - K2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.64', '6.74', '6.106', '6.178', '6.300', '6.397', '6.479', '6.481', '6.500'] |
| Outer characteristic polynomial of the knot is: t^7+95t^5+136t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.481'] |
| 2-strand cable arrow polynomial of the knot is: -1312*K1**2*K2**2 - 704*K1**2*K2*K4 + 2056*K1**2*K2 - 128*K1**2*K3**2 - 2448*K1**2 + 256*K1*K2**3*K3 + 160*K1*K2**2*K3*K4 - 352*K1*K2**2*K3 - 32*K1*K2**2*K5 - 224*K1*K2*K3*K4 + 3456*K1*K2*K3 + 944*K1*K3*K4 + 48*K1*K4*K5 - 32*K2**4*K4**2 + 128*K2**4*K4 - 544*K2**4 + 32*K2**3*K4*K6 - 32*K2**3*K6 - 1024*K2**2*K3**2 - 432*K2**2*K4**2 + 1224*K2**2*K4 - 8*K2**2*K6**2 - 1992*K2**2 + 728*K2*K3*K5 + 208*K2*K4*K6 - 1304*K3**2 - 610*K4**2 - 120*K5**2 - 24*K6**2 + 2080 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.481'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.74156', 'vk6.74160', 'vk6.74754', 'vk6.74762', 'vk6.76288', 'vk6.76296', 'vk6.76824', 'vk6.76830', 'vk6.79184', 'vk6.79190', 'vk6.79654', 'vk6.79660', 'vk6.80672', 'vk6.80676', 'vk6.81044', 'vk6.81048', 'vk6.82882', 'vk6.82910', 'vk6.83104', 'vk6.83344', 'vk6.83402', 'vk6.84172', 'vk6.84280', 'vk6.85567', 'vk6.85630', 'vk6.85877', 'vk6.86202', 'vk6.86631', 'vk6.87497', 'vk6.88147', 'vk6.88584', 'vk6.89392'] |
| 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 | O1O2O3O4O5U1U3U2O6U5U4U6 |
| R3 orbit | {'O1O2O3O4O5U1U3U2O6U5U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U6U2U1O6U4U3U5 |
| Gauss code of K* | O1O2O3U4O5O6O4U1U3U2U6U5 |
| Gauss code of -K* | O1O2O3U1O4O5O6U3U2U5U4U6 |
| 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 -4 -1 -1 2 2 2],[ 4 0 2 1 4 3 2],[ 1 -2 0 0 3 2 2],[ 1 -1 0 0 2 1 2],[-2 -4 -3 -2 0 0 2],[-2 -3 -2 -1 0 0 1],[-2 -2 -2 -2 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 2 2 -1 -1 -4],[-2 0 2 0 -2 -3 -4],[-2 -2 0 -1 -2 -2 -2],[-2 0 1 0 -1 -2 -3],[ 1 2 2 1 0 0 -1],[ 1 3 2 2 0 0 -2],[ 4 4 2 3 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-2,1,1,4,-2,0,2,3,4,1,2,2,2,1,2,3,0,1,2] |
| Phi over symmetry | [-4,-1,-1,2,2,2,1,2,2,3,4,0,0,1,1,1,2,1,0,-2,-1] |
| Phi of -K | [-4,-1,-1,2,2,2,1,2,2,3,4,0,0,1,1,1,2,1,0,-2,-1] |
| Phi of K* | [-2,-2,-2,1,1,4,-2,-1,1,1,4,0,0,1,2,1,2,3,0,1,2] |
| Phi of -K* | [-4,-1,-1,2,2,2,1,2,2,3,4,0,2,1,2,2,2,3,-1,-2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^4-3t^2+2t |
| Normalized Jones-Krushkal polynomial | 6z^2+19z+15 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+8w^3z^2-6w^3z+25w^2z+15w |
| Inner characteristic polynomial | t^6+65t^4+41t^2+1 |
| Outer characteristic polynomial | t^7+95t^5+136t^3+8t |
| Flat arrow polynomial | 4*K1**2*K2 - 2*K1*K3 - K2 |
| 2-strand cable arrow polynomial | -1312*K1**2*K2**2 - 704*K1**2*K2*K4 + 2056*K1**2*K2 - 128*K1**2*K3**2 - 2448*K1**2 + 256*K1*K2**3*K3 + 160*K1*K2**2*K3*K4 - 352*K1*K2**2*K3 - 32*K1*K2**2*K5 - 224*K1*K2*K3*K4 + 3456*K1*K2*K3 + 944*K1*K3*K4 + 48*K1*K4*K5 - 32*K2**4*K4**2 + 128*K2**4*K4 - 544*K2**4 + 32*K2**3*K4*K6 - 32*K2**3*K6 - 1024*K2**2*K3**2 - 432*K2**2*K4**2 + 1224*K2**2*K4 - 8*K2**2*K6**2 - 1992*K2**2 + 728*K2*K3*K5 + 208*K2*K4*K6 - 1304*K3**2 - 610*K4**2 - 120*K5**2 - 24*K6**2 + 2080 |
| 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}], [{1, 6}, {5}, {4}, {3}, {2}], [{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}], [{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}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {2, 3}, {1}]] |
| If K is slice | False |