| Min(phi) over symmetries of the knot is: [-3,-1,0,0,2,2,0,1,2,2,2,1,0,1,1,0,0,0,1,2,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.991'] |
| Arrow polynomial of the knot is: -4*K1**2 - 6*K1*K2 + 3*K1 + 2*K2 + 3*K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.586', '6.590', '6.958', '6.987', '6.991', '6.993', '6.999', '6.1054', '6.1065', '6.1096', '6.1168', '6.1182'] |
| Outer characteristic polynomial of the knot is: t^7+63t^5+83t^3+13t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.991'] |
| 2-strand cable arrow polynomial of the knot is: -576*K1**4 + 480*K1**3*K2*K3 - 384*K1**3*K3 - 192*K1**2*K2**2*K3**2 - 3184*K1**2*K2**2 + 256*K1**2*K2*K3**2 - 160*K1**2*K2*K4 + 4800*K1**2*K2 - 1008*K1**2*K3**2 - 4852*K1**2 + 608*K1*K2**3*K3 - 864*K1*K2**2*K3 - 96*K1*K2**2*K5 + 128*K1*K2*K3**3 - 384*K1*K2*K3*K4 + 7328*K1*K2*K3 + 1136*K1*K3*K4 + 40*K1*K4*K5 - 480*K2**4 - 864*K2**2*K3**2 - 56*K2**2*K4**2 + 768*K2**2*K4 - 3762*K2**2 + 512*K2*K3*K5 + 40*K2*K4*K6 - 16*K3**4 - 2668*K3**2 - 396*K4**2 - 40*K5**2 - 6*K6**2 + 3890 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.991'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73337', 'vk6.73338', 'vk6.73498', 'vk6.73500', 'vk6.75260', 'vk6.75261', 'vk6.75506', 'vk6.75508', 'vk6.78223', 'vk6.78225', 'vk6.78465', 'vk6.78466', 'vk6.80048', 'vk6.80050', 'vk6.80197', 'vk6.80198', 'vk6.81931', 'vk6.81938', 'vk6.82192', 'vk6.82210', 'vk6.82655', 'vk6.82666', 'vk6.84721', 'vk6.84724', 'vk6.85021', 'vk6.85028', 'vk6.85756', 'vk6.86504', 'vk6.87331', 'vk6.87695', 'vk6.89624', 'vk6.90083'] |
| 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 | O1O2O3O4U1U5O6U3O5U2U4U6 |
| R3 orbit | {'O1O2O3O4U1U5O6U3O5U2U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U1U3O6U2O5U6U4 |
| Gauss code of K* | O1O2O3U4U1U5U2O4O6U3O5U6 |
| Gauss code of -K* | O1O2O3U4O5U1O4O6U2U5U3U6 |
| 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 -1 0 2 0 2],[ 3 0 2 1 3 2 3],[ 1 -2 0 1 2 0 2],[ 0 -1 -1 0 0 0 1],[-2 -3 -2 0 0 -2 0],[ 0 -2 0 0 2 0 2],[-2 -3 -2 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 2 0 0 -1 -3],[-2 0 0 0 -2 -2 -3],[-2 0 0 -1 -2 -2 -3],[ 0 0 1 0 0 -1 -1],[ 0 2 2 0 0 0 -2],[ 1 2 2 1 0 0 -2],[ 3 3 3 1 2 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,0,1,3,0,0,2,2,3,1,2,2,3,0,1,1,0,2,2] |
| Phi over symmetry | [-3,-1,0,0,2,2,0,1,2,2,2,1,0,1,1,0,0,0,1,2,0] |
| Phi of -K | [-3,-1,0,0,2,2,0,1,2,2,2,1,0,1,1,0,0,0,1,2,0] |
| Phi of K* | [-2,-2,0,0,1,3,0,0,1,1,2,0,2,1,2,0,1,1,0,2,0] |
| Phi of -K* | [-3,-1,0,0,2,2,2,1,2,3,3,1,0,2,2,0,0,1,2,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-2t^2+t |
| Normalized Jones-Krushkal polynomial | 5z^2+26z+33 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+26w^2z+33w |
| Inner characteristic polynomial | t^6+45t^4+43t^2 |
| Outer characteristic polynomial | t^7+63t^5+83t^3+13t |
| Flat arrow polynomial | -4*K1**2 - 6*K1*K2 + 3*K1 + 2*K2 + 3*K3 + 3 |
| 2-strand cable arrow polynomial | -576*K1**4 + 480*K1**3*K2*K3 - 384*K1**3*K3 - 192*K1**2*K2**2*K3**2 - 3184*K1**2*K2**2 + 256*K1**2*K2*K3**2 - 160*K1**2*K2*K4 + 4800*K1**2*K2 - 1008*K1**2*K3**2 - 4852*K1**2 + 608*K1*K2**3*K3 - 864*K1*K2**2*K3 - 96*K1*K2**2*K5 + 128*K1*K2*K3**3 - 384*K1*K2*K3*K4 + 7328*K1*K2*K3 + 1136*K1*K3*K4 + 40*K1*K4*K5 - 480*K2**4 - 864*K2**2*K3**2 - 56*K2**2*K4**2 + 768*K2**2*K4 - 3762*K2**2 + 512*K2*K3*K5 + 40*K2*K4*K6 - 16*K3**4 - 2668*K3**2 - 396*K4**2 - 40*K5**2 - 6*K6**2 + 3890 |
| 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}], [{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}]] |
| If K is slice | False |