| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,0,1,1,2,-1,-1,1,0,0,0,1,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1587'] |
| 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+19t^5+47t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1587'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 768*K1**4*K2 - 3536*K1**4 + 384*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1248*K1**3*K3 - 2352*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 352*K1**2*K2*K4 + 9080*K1**2*K2 - 880*K1**2*K3**2 - 80*K1**2*K4**2 - 6228*K1**2 - 704*K1*K2**2*K3 - 192*K1*K2*K3*K4 + 6128*K1*K2*K3 + 1480*K1*K3*K4 + 112*K1*K4*K5 - 72*K2**4 - 160*K2**2*K3**2 - 48*K2**2*K4**2 + 768*K2**2*K4 - 5020*K2**2 + 200*K2*K3*K5 + 32*K2*K4*K6 - 2328*K3**2 - 662*K4**2 - 60*K5**2 - 4*K6**2 + 5004 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1587'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3650', 'vk6.3745', 'vk6.3936', 'vk6.4031', 'vk6.4477', 'vk6.4574', 'vk6.5859', 'vk6.5988', 'vk6.7141', 'vk6.7316', 'vk6.7407', 'vk6.7908', 'vk6.8029', 'vk6.9338', 'vk6.17927', 'vk6.18022', 'vk6.18757', 'vk6.24462', 'vk6.24878', 'vk6.25339', 'vk6.37504', 'vk6.43897', 'vk6.44233', 'vk6.44536', 'vk6.48274', 'vk6.48337', 'vk6.50063', 'vk6.50173', 'vk6.50569', 'vk6.50634', 'vk6.55870', 'vk6.60733'] |
| 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 | O1O2O3U4O5U3U5O6O4U1U6U2 |
| R3 orbit | {'O1O2O3U4O5U3U5O6O4U1U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U4U3O5O4U6U1O6U5 |
| Gauss code of K* | O1O2O3U1U3U4O5U6O4O6U2U5 |
| Gauss code of -K* | O1O2O3U4U2O5O6U5O4U6U1U3 |
| 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 0 0 1 0],[ 2 0 2 0 1 1 0],[-1 -2 0 0 -1 1 -1],[ 0 0 0 0 -1 1 -1],[ 0 -1 1 1 0 1 0],[-1 -1 -1 -1 -1 0 0],[ 0 0 1 1 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 0 -2],[-1 0 1 0 -1 -1 -2],[-1 -1 0 -1 0 -1 -1],[ 0 0 1 0 -1 -1 0],[ 0 1 0 1 0 0 0],[ 0 1 1 1 0 0 -1],[ 2 2 1 0 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,0,2,-1,0,1,1,2,1,0,1,1,1,1,0,0,0,1] |
| Phi over symmetry | [-2,0,0,0,1,1,0,0,1,1,2,-1,-1,1,0,0,0,1,1,1,-1] |
| Phi of -K | [-2,0,0,0,1,1,1,2,2,1,2,-1,0,0,0,1,1,0,0,1,-1] |
| Phi of K* | [-1,-1,0,0,0,2,-1,0,0,1,2,0,1,0,1,1,0,1,-1,2,2] |
| Phi of -K* | [-2,0,0,0,1,1,0,0,1,1,2,-1,-1,1,0,0,0,1,1,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 19z+39 |
| Enhanced Jones-Krushkal polynomial | 19w^2z+39w |
| Inner characteristic polynomial | t^6+13t^4+22t^2+4 |
| Outer characteristic polynomial | t^7+19t^5+47t^3+9t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -128*K1**6 + 768*K1**4*K2 - 3536*K1**4 + 384*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1248*K1**3*K3 - 2352*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 352*K1**2*K2*K4 + 9080*K1**2*K2 - 880*K1**2*K3**2 - 80*K1**2*K4**2 - 6228*K1**2 - 704*K1*K2**2*K3 - 192*K1*K2*K3*K4 + 6128*K1*K2*K3 + 1480*K1*K3*K4 + 112*K1*K4*K5 - 72*K2**4 - 160*K2**2*K3**2 - 48*K2**2*K4**2 + 768*K2**2*K4 - 5020*K2**2 + 200*K2*K3*K5 + 32*K2*K4*K6 - 2328*K3**2 - 662*K4**2 - 60*K5**2 - 4*K6**2 + 5004 |
| 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}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {1, 5}, {4}, {3}, {2}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {2, 5}, {4}, {3}, {1}], [{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}, {4, 5}, {3}, {2}, {1}], [{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 |