| Min(phi) over symmetries of the knot is: [-3,-2,1,1,1,2,0,1,2,3,3,0,1,2,2,-1,-1,-1,0,1,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.739'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1*K2 - 2*K1 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.233', '6.340', '6.382', '6.550', '6.656', '6.663', '6.683', '6.698', '6.739', '6.745', '6.759', '6.765', '6.1357', '6.1358', '6.1370'] |
| Outer characteristic polynomial of the knot is: t^7+60t^5+60t^3+15t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.739'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**2*K2**4 + 1824*K1**2*K2**3 + 256*K1**2*K2**2*K4 - 6736*K1**2*K2**2 - 768*K1**2*K2*K4 + 6648*K1**2*K2 - 192*K1**2*K4**2 - 4536*K1**2 + 352*K1*K2**3*K3 - 1536*K1*K2**2*K3 - 96*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 5640*K1*K2*K3 + 832*K1*K3*K4 + 184*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 1376*K2**4 - 112*K2**2*K3**2 - 8*K2**2*K4**2 + 1640*K2**2*K4 - 2736*K2**2 + 128*K2*K3*K5 - 1192*K3**2 - 520*K4**2 - 56*K5**2 + 2998 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.739'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16996', 'vk6.17238', 'vk6.20527', 'vk6.21923', 'vk6.23404', 'vk6.23713', 'vk6.27981', 'vk6.29450', 'vk6.35468', 'vk6.35914', 'vk6.39385', 'vk6.41574', 'vk6.42905', 'vk6.43205', 'vk6.45962', 'vk6.47639', 'vk6.55171', 'vk6.55416', 'vk6.57397', 'vk6.58572', 'vk6.59554', 'vk6.59893', 'vk6.62066', 'vk6.63051', 'vk6.64975', 'vk6.65184', 'vk6.66943', 'vk6.67802', 'vk6.68268', 'vk6.68423', 'vk6.69557', 'vk6.70253'] |
| 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 | O1O2O3O4U2O5U1U4U3O6U5U6 |
| R3 orbit | {'O1O2O3O4U2O5U1U4U3O6U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6O5U2U1U4O6U3 |
| Gauss code of K* | O1O2O3U4O5O4U1U6U3U2O6U5 |
| Gauss code of -K* | O1O2O3U4O5U2U1U5U3O6O4U6 |
| 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 1 1 2 1],[ 3 0 0 3 2 3 1],[ 2 0 0 2 1 2 0],[-1 -3 -2 0 0 2 1],[-1 -2 -1 0 0 1 1],[-2 -3 -2 -2 -1 0 1],[-1 -1 0 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 1 -2 -3],[-2 0 1 -1 -2 -2 -3],[-1 -1 0 -1 -1 0 -1],[-1 1 1 0 0 -1 -2],[-1 2 1 0 0 -2 -3],[ 2 2 0 1 2 0 0],[ 3 3 1 2 3 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,-1,2,3,-1,1,2,2,3,1,1,0,1,0,1,2,2,3,0] |
| Phi over symmetry | [-3,-2,1,1,1,2,0,1,2,3,3,0,1,2,2,-1,-1,-1,0,1,2] |
| Phi of -K | [-3,-2,1,1,1,2,1,1,2,3,2,1,2,3,2,0,-1,-1,-1,0,2] |
| Phi of K* | [-2,-1,-1,-1,2,3,-1,0,2,2,2,0,1,1,1,1,2,2,3,3,1] |
| Phi of -K* | [-3,-2,1,1,1,2,0,1,2,3,3,0,1,2,2,-1,-1,-1,0,1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-3t |
| Normalized Jones-Krushkal polynomial | 6z^2+19z+15 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+8w^3z^2-8w^3z+27w^2z+15w |
| Inner characteristic polynomial | t^6+40t^4+20t^2 |
| Outer characteristic polynomial | t^7+60t^5+60t^3+15t |
| Flat arrow polynomial | 4*K1**3 - 2*K1*K2 - 2*K1 + 1 |
| 2-strand cable arrow polynomial | -448*K1**2*K2**4 + 1824*K1**2*K2**3 + 256*K1**2*K2**2*K4 - 6736*K1**2*K2**2 - 768*K1**2*K2*K4 + 6648*K1**2*K2 - 192*K1**2*K4**2 - 4536*K1**2 + 352*K1*K2**3*K3 - 1536*K1*K2**2*K3 - 96*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 5640*K1*K2*K3 + 832*K1*K3*K4 + 184*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 1376*K2**4 - 112*K2**2*K3**2 - 8*K2**2*K4**2 + 1640*K2**2*K4 - 2736*K2**2 + 128*K2*K3*K5 - 1192*K3**2 - 520*K4**2 - 56*K5**2 + 2998 |
| 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}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |