| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-2,0,1,2,3,1,1,2,2,1,1,1,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.372'] |
| Arrow polynomial of the knot is: -10*K1**2 - 8*K1*K2 + 4*K1 + 5*K2 + 4*K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.372', '6.930', '6.1007', '6.1701', '6.1714', '6.1760', '6.1788'] |
| Outer characteristic polynomial of the knot is: t^7+41t^5+58t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.372', '7.21437'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 640*K1**4*K2 - 2880*K1**4 + 256*K1**3*K2*K3 - 896*K1**3*K3 - 2672*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 192*K1**2*K2*K4 + 7704*K1**2*K2 - 1760*K1**2*K3**2 - 256*K1**2*K4**2 - 5824*K1**2 - 800*K1*K2**2*K3 - 128*K1*K2**2*K5 + 64*K1*K2*K3**3 - 448*K1*K2*K3*K4 - 96*K1*K2*K3*K6 + 7232*K1*K2*K3 + 2656*K1*K3*K4 + 504*K1*K4*K5 + 32*K1*K5*K6 - 232*K2**4 - 688*K2**2*K3**2 - 96*K2**2*K4**2 + 1064*K2**2*K4 - 4912*K2**2 - 128*K2*K3**2*K4 + 960*K2*K3*K5 + 168*K2*K4*K6 - 160*K3**4 + 200*K3**2*K6 - 2924*K3**2 - 1138*K4**2 - 364*K5**2 - 88*K6**2 + 5232 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.372'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3654', 'vk6.3749', 'vk6.3940', 'vk6.4035', 'vk6.4485', 'vk6.4582', 'vk6.5867', 'vk6.5996', 'vk6.7137', 'vk6.7312', 'vk6.7403', 'vk6.7916', 'vk6.8037', 'vk6.9346', 'vk6.17931', 'vk6.18026', 'vk6.18761', 'vk6.24466', 'vk6.24882', 'vk6.25343', 'vk6.37500', 'vk6.43893', 'vk6.44229', 'vk6.44532', 'vk6.48278', 'vk6.48341', 'vk6.50059', 'vk6.50169', 'vk6.50561', 'vk6.50626', 'vk6.55874', 'vk6.60737'] |
| 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 | O1O2O3O4O5U3U5O6U4U1U6U2 |
| R3 orbit | {'O1O2O3O4O5U3U5O6U4U1U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U4U6U5U2O6U1U3 |
| Gauss code of K* | O1O2O3O4U2U4U5U1U6O5O6U3 |
| Gauss code of -K* | O1O2O3O4U2O5O6U5U4U6U1U3 |
| 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 -2 0 1 2],[ 2 0 2 -2 1 1 2],[-1 -2 0 -2 0 1 1],[ 2 2 2 0 2 1 1],[ 0 -1 0 -2 0 0 1],[-1 -1 -1 -1 0 0 0],[-2 -2 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 0 -1 -1 -1 -2],[-1 0 0 -1 0 -1 -1],[-1 1 1 0 0 -2 -2],[ 0 1 0 0 0 -2 -1],[ 2 1 1 2 2 0 2],[ 2 2 1 2 1 -2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,0,1,1,1,2,1,0,1,1,0,2,2,2,1,-2] |
| Phi over symmetry | [-2,-2,0,1,1,2,-2,0,1,2,3,1,1,2,2,1,1,1,-1,0,1] |
| Phi of -K | [-2,-2,0,1,1,2,-2,0,1,2,3,1,1,2,2,1,1,1,-1,0,1] |
| Phi of K* | [-2,-1,-1,0,2,2,0,1,1,2,3,1,1,1,1,1,2,2,1,0,-2] |
| Phi of -K* | [-2,-2,0,1,1,2,-2,1,1,2,2,2,1,2,1,0,0,1,-1,0,1] |
| 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+27t^4+21t^2 |
| Outer characteristic polynomial | t^7+41t^5+58t^3+5t |
| Flat arrow polynomial | -10*K1**2 - 8*K1*K2 + 4*K1 + 5*K2 + 4*K3 + 6 |
| 2-strand cable arrow polynomial | -128*K1**6 + 640*K1**4*K2 - 2880*K1**4 + 256*K1**3*K2*K3 - 896*K1**3*K3 - 2672*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 192*K1**2*K2*K4 + 7704*K1**2*K2 - 1760*K1**2*K3**2 - 256*K1**2*K4**2 - 5824*K1**2 - 800*K1*K2**2*K3 - 128*K1*K2**2*K5 + 64*K1*K2*K3**3 - 448*K1*K2*K3*K4 - 96*K1*K2*K3*K6 + 7232*K1*K2*K3 + 2656*K1*K3*K4 + 504*K1*K4*K5 + 32*K1*K5*K6 - 232*K2**4 - 688*K2**2*K3**2 - 96*K2**2*K4**2 + 1064*K2**2*K4 - 4912*K2**2 - 128*K2*K3**2*K4 + 960*K2*K3*K5 + 168*K2*K4*K6 - 160*K3**4 + 200*K3**2*K6 - 2924*K3**2 - 1138*K4**2 - 364*K5**2 - 88*K6**2 + 5232 |
| 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}], [{5, 6}, {4}, {3}, {2}, {1}], [{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}, {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 |