| Min(phi) over symmetries of the knot is: [-4,-1,0,0,2,3,0,1,2,5,3,0,0,1,0,0,1,1,1,2,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.511'] |
| Arrow polynomial of the knot is: -2*K1*K2 - 2*K1*K3 + K1 + K2 + K3 + K4 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.58', '6.76', '6.78', '6.90', '6.98', '6.154', '6.161', '6.162', '6.198', '6.280', '6.284', '6.345', '6.417', '6.421', '6.435', '6.511'] |
| Outer characteristic polynomial of the knot is: t^7+99t^5+54t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.511'] |
| 2-strand cable arrow polynomial of the knot is: -1312*K1**3*K3 - 192*K1**2*K2**2 + 256*K1**2*K2*K3**2 + 3272*K1**2*K2 - 2528*K1**2*K3**2 - 320*K1**2*K3*K5 - 64*K1**2*K4*K6 - 48*K1**2*K6**2 - 4976*K1**2 + 64*K1*K2**3*K3 - 544*K1*K2**2*K3 + 128*K1*K2*K3**3 - 224*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 6568*K1*K2*K3 - 128*K1*K3**2*K5 - 32*K1*K3*K4*K6 + 2496*K1*K3*K4 + 312*K1*K4*K5 + 200*K1*K5*K6 + 40*K1*K6*K7 - 64*K2**4 - 640*K2**2*K3**2 - 8*K2**2*K4**2 + 296*K2**2*K4 - 8*K2**2*K6**2 - 3210*K2**2 + 832*K2*K3*K5 + 80*K2*K4*K6 + 8*K2*K6*K8 - 128*K3**4 + 160*K3**2*K6 - 2792*K3**2 + 8*K3*K4*K7 - 638*K4**2 - 340*K5**2 - 126*K6**2 - 4*K7**2 - 2*K8**2 + 3670 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.511'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4651', 'vk6.4936', 'vk6.6097', 'vk6.6588', 'vk6.8112', 'vk6.8514', 'vk6.9504', 'vk6.9861', 'vk6.20622', 'vk6.22049', 'vk6.28108', 'vk6.29549', 'vk6.39524', 'vk6.41747', 'vk6.46135', 'vk6.47777', 'vk6.48683', 'vk6.48880', 'vk6.49431', 'vk6.49658', 'vk6.50697', 'vk6.50892', 'vk6.51182', 'vk6.51389', 'vk6.57514', 'vk6.58702', 'vk6.62210', 'vk6.63156', 'vk6.67024', 'vk6.67897', 'vk6.69653', 'vk6.70334'] |
| 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 | O1O2O3O4O5U1U6U5O6U3U2U4 |
| R3 orbit | {'O1O2O3O4O5U1U6U5O6U3U2U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U2U4U3O6U1U6U5 |
| Gauss code of K* | O1O2O3U2O4O5O6U1U5U4U6U3 |
| Gauss code of -K* | O1O2O3U4O5O4O6U5U1U3U2U6 |
| 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 0 0 3 2 -1],[ 4 0 3 2 4 1 3],[ 0 -3 0 0 2 1 -1],[ 0 -2 0 0 1 1 -1],[-3 -4 -2 -1 0 1 -4],[-2 -1 -1 -1 -1 0 -2],[ 1 -3 1 1 4 2 0]] |
| Primitive based matrix | [[ 0 3 2 0 0 -1 -4],[-3 0 1 -1 -2 -4 -4],[-2 -1 0 -1 -1 -2 -1],[ 0 1 1 0 0 -1 -2],[ 0 2 1 0 0 -1 -3],[ 1 4 2 1 1 0 -3],[ 4 4 1 2 3 3 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,0,1,4,-1,1,2,4,4,1,1,2,1,0,1,2,1,3,3] |
| Phi over symmetry | [-4,-1,0,0,2,3,0,1,2,5,3,0,0,1,0,0,1,1,1,2,2] |
| Phi of -K | [-4,-1,0,0,2,3,0,1,2,5,3,0,0,1,0,0,1,1,1,2,2] |
| Phi of K* | [-3,-2,0,0,1,4,2,1,2,0,3,1,1,1,5,0,0,1,0,2,0] |
| Phi of -K* | [-4,-1,0,0,2,3,3,2,3,1,4,1,1,2,4,0,1,1,1,2,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^4-t^3-t^2+t |
| Normalized Jones-Krushkal polynomial | 4z^2+23z+31 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+23w^2z+31w |
| Inner characteristic polynomial | t^6+69t^4+19t^2+1 |
| Outer characteristic polynomial | t^7+99t^5+54t^3+6t |
| Flat arrow polynomial | -2*K1*K2 - 2*K1*K3 + K1 + K2 + K3 + K4 + 1 |
| 2-strand cable arrow polynomial | -1312*K1**3*K3 - 192*K1**2*K2**2 + 256*K1**2*K2*K3**2 + 3272*K1**2*K2 - 2528*K1**2*K3**2 - 320*K1**2*K3*K5 - 64*K1**2*K4*K6 - 48*K1**2*K6**2 - 4976*K1**2 + 64*K1*K2**3*K3 - 544*K1*K2**2*K3 + 128*K1*K2*K3**3 - 224*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 6568*K1*K2*K3 - 128*K1*K3**2*K5 - 32*K1*K3*K4*K6 + 2496*K1*K3*K4 + 312*K1*K4*K5 + 200*K1*K5*K6 + 40*K1*K6*K7 - 64*K2**4 - 640*K2**2*K3**2 - 8*K2**2*K4**2 + 296*K2**2*K4 - 8*K2**2*K6**2 - 3210*K2**2 + 832*K2*K3*K5 + 80*K2*K4*K6 + 8*K2*K6*K8 - 128*K3**4 + 160*K3**2*K6 - 2792*K3**2 + 8*K3*K4*K7 - 638*K4**2 - 340*K5**2 - 126*K6**2 - 4*K7**2 - 2*K8**2 + 3670 |
| 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}], [{2, 6}, {5}, {4}, {3}, {1}], [{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}, {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}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {2, 3}, {1}]] |
| If K is slice | False |