| Min(phi) over symmetries of the knot is: [-3,-2,1,1,1,2,0,1,3,4,2,0,1,2,2,0,0,0,0,1,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.656'] |
| 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+64t^5+114t^3+10t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.656'] |
| 2-strand cable arrow polynomial of the knot is: -576*K1**2*K2**4 + 1184*K1**2*K2**3 - 5136*K1**2*K2**2 - 32*K1**2*K2*K4 + 4256*K1**2*K2 - 2568*K1**2 + 512*K1*K2**3*K3 - 576*K1*K2**2*K3 + 3680*K1*K2*K3 + 32*K1*K3*K4 - 288*K2**6 + 160*K2**4*K4 - 1504*K2**4 - 112*K2**2*K3**2 - 8*K2**2*K4**2 + 984*K2**2*K4 - 944*K2**2 - 664*K3**2 - 88*K4**2 + 1686 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.656'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17536', 'vk6.17544', 'vk6.17593', 'vk6.17601', 'vk6.24042', 'vk6.24052', 'vk6.24136', 'vk6.24144', 'vk6.36320', 'vk6.36332', 'vk6.36393', 'vk6.36399', 'vk6.43445', 'vk6.43453', 'vk6.43494', 'vk6.43499', 'vk6.55634', 'vk6.55642', 'vk6.55659', 'vk6.55667', 'vk6.60152', 'vk6.60157', 'vk6.60207', 'vk6.60217', 'vk6.65339', 'vk6.65345', 'vk6.65369', 'vk6.65377', 'vk6.68505', 'vk6.68509', 'vk6.68527', 'vk6.68533'] |
| 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 | O1O2O3O4U2O5U1U5O6U4U3U6 |
| R3 orbit | {'O1O2O3O4U2O5U1U5O6U4U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U2U1O5U6U4O6U3 |
| Gauss code of K* | O1O2O3U4U5U2U1O5U6O4O6U3 |
| Gauss code of -K* | O1O2O3U1O4O5U4O6U3U2U6U5 |
| 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 1 2],[ 3 0 0 4 3 1 2],[ 2 0 0 2 1 0 2],[-1 -4 -2 0 0 0 2],[-1 -3 -1 0 0 0 1],[-1 -1 0 0 0 0 0],[-2 -2 -2 -2 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 1 -2 -3],[-2 0 0 -1 -2 -2 -2],[-1 0 0 0 0 0 -1],[-1 1 0 0 0 -1 -3],[-1 2 0 0 0 -2 -4],[ 2 2 0 1 2 0 0],[ 3 2 1 3 4 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,-1,2,3,0,1,2,2,2,0,0,0,1,0,1,3,2,4,0] |
| Phi over symmetry | [-3,-2,1,1,1,2,0,1,3,4,2,0,1,2,2,0,0,0,0,1,2] |
| Phi of -K | [-3,-2,1,1,1,2,1,0,1,3,3,1,2,3,2,0,0,-1,0,0,1] |
| Phi of K* | [-2,-1,-1,-1,2,3,-1,0,1,2,3,0,0,1,0,0,2,1,3,3,1] |
| Phi of -K* | [-3,-2,1,1,1,2,0,1,3,4,2,0,1,2,2,0,0,0,0,1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-3t |
| Normalized Jones-Krushkal polynomial | 2z^2+7z+7 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+6w^3z^2-12w^3z+19w^2z+7w |
| Inner characteristic polynomial | t^6+44t^4+54t^2 |
| Outer characteristic polynomial | t^7+64t^5+114t^3+10t |
| Flat arrow polynomial | 4*K1**3 - 2*K1*K2 - 2*K1 + 1 |
| 2-strand cable arrow polynomial | -576*K1**2*K2**4 + 1184*K1**2*K2**3 - 5136*K1**2*K2**2 - 32*K1**2*K2*K4 + 4256*K1**2*K2 - 2568*K1**2 + 512*K1*K2**3*K3 - 576*K1*K2**2*K3 + 3680*K1*K2*K3 + 32*K1*K3*K4 - 288*K2**6 + 160*K2**4*K4 - 1504*K2**4 - 112*K2**2*K3**2 - 8*K2**2*K4**2 + 984*K2**2*K4 - 944*K2**2 - 664*K3**2 - 88*K4**2 + 1686 |
| 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}], [{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}, {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}, {3, 4}, {1, 2}]] |
| If K is slice | False |