| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,2,1,2,4,1,1,1,2,1,2,2,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.593'] |
| Arrow polynomial of the knot is: -10*K1**2 - 2*K1*K2 + K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.574', '6.593', '6.604', '6.649', '6.650', '6.673', '6.690', '6.783', '6.973', '6.985', '6.1033', '6.1035'] |
| Outer characteristic polynomial of the knot is: t^7+65t^5+48t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.593'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 768*K1**4*K2 - 1936*K1**4 + 160*K1**3*K2*K3 + 32*K1**3*K3*K4 - 288*K1**3*K3 + 160*K1**2*K2**3 - 3216*K1**2*K2**2 - 320*K1**2*K2*K4 + 7064*K1**2*K2 - 272*K1**2*K3**2 - 32*K1**2*K4**2 - 5368*K1**2 - 160*K1*K2**2*K3 + 4264*K1*K2*K3 + 776*K1*K3*K4 + 56*K1*K4*K5 - 152*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 408*K2**2*K4 - 3766*K2**2 + 64*K2*K3*K5 + 8*K2*K4*K6 - 1468*K3**2 - 418*K4**2 - 44*K5**2 - 2*K6**2 + 3928 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.593'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17096', 'vk6.17337', 'vk6.20591', 'vk6.21999', 'vk6.23485', 'vk6.23822', 'vk6.28056', 'vk6.29514', 'vk6.35626', 'vk6.36069', 'vk6.39463', 'vk6.41664', 'vk6.42996', 'vk6.43306', 'vk6.46051', 'vk6.47719', 'vk6.55247', 'vk6.55497', 'vk6.57461', 'vk6.58627', 'vk6.59651', 'vk6.59997', 'vk6.62136', 'vk6.63100', 'vk6.65043', 'vk6.65240', 'vk6.66987', 'vk6.67851', 'vk6.68310', 'vk6.68458', 'vk6.69605', 'vk6.70297'] |
| 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 | O1O2O3O4U2O5U1O6U4U6U5U3 |
| R3 orbit | {'O1O2O3O4U2O5U1O6U4U6U5U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U6U1O6U4O5U3 |
| Gauss code of K* | O1O2O3O4U5U6U4U1O6U3O5U2 |
| Gauss code of -K* | O1O2O3O4U3O5U2O6U4U1U6U5 |
| 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 -3 -2 2 0 2 1],[ 3 0 0 4 2 2 1],[ 2 0 0 2 1 1 1],[-2 -4 -2 0 -2 1 1],[ 0 -2 -1 2 0 2 1],[-2 -2 -1 -1 -2 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 1 1 -2 -2 -4],[-2 -1 0 0 -2 -1 -2],[-1 -1 0 0 -1 -1 -1],[ 0 2 2 1 0 -1 -2],[ 2 2 1 1 1 0 0],[ 3 4 2 1 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,-1,-1,2,2,4,0,2,1,2,1,1,1,1,2,0] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,2,1,2,4,1,1,1,2,1,2,2,0,-1,-1] |
| Phi of -K | [-3,-2,0,1,2,2,1,1,3,1,3,1,2,2,3,0,0,0,2,1,-1] |
| Phi of K* | [-2,-2,-1,0,2,3,-1,1,0,3,3,2,0,2,1,0,2,3,1,1,1] |
| Phi of -K* | [-3,-2,0,1,2,2,0,2,1,2,4,1,1,1,2,1,2,2,0,-1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 2z^2+21z+35 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+21w^2z+35w |
| Inner characteristic polynomial | t^6+43t^4+15t^2+1 |
| Outer characteristic polynomial | t^7+65t^5+48t^3+6t |
| Flat arrow polynomial | -10*K1**2 - 2*K1*K2 + K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 768*K1**4*K2 - 1936*K1**4 + 160*K1**3*K2*K3 + 32*K1**3*K3*K4 - 288*K1**3*K3 + 160*K1**2*K2**3 - 3216*K1**2*K2**2 - 320*K1**2*K2*K4 + 7064*K1**2*K2 - 272*K1**2*K3**2 - 32*K1**2*K4**2 - 5368*K1**2 - 160*K1*K2**2*K3 + 4264*K1*K2*K3 + 776*K1*K3*K4 + 56*K1*K4*K5 - 152*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 408*K2**2*K4 - 3766*K2**2 + 64*K2*K3*K5 + 8*K2*K4*K6 - 1468*K3**2 - 418*K4**2 - 44*K5**2 - 2*K6**2 + 3928 |
| 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}], [{3, 6}, {5}, {4}, {2}, {1}], [{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}, {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}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {1, 3}, {2}]] |
| If K is slice | False |