| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,2,3,2,3,2,2,1,2,0,1,1,2,2,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.217'] |
| Arrow polynomial of the knot is: -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.217', '6.219', '6.304', '6.349', '6.390', '6.400', '6.416', '6.515', '6.518', '6.530', '6.582', '6.616', '6.629', '6.641', '6.645', '6.702', '6.710', '6.715', '6.729', '6.733', '6.734', '6.802', '6.840', '6.845', '6.854', '6.860', '6.900', '6.905', '6.921', '6.924', '6.979', '6.980', '6.996', '6.1044', '6.1067', '6.1086', '6.1100', '6.1139', '6.1145', '6.1149', '6.1167', '6.1169', '6.1183', '6.1314'] |
| Outer characteristic polynomial of the knot is: t^7+57t^5+68t^3+13t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.217'] |
| 2-strand cable arrow polynomial of the knot is: 96*K1**4*K2 - 128*K1**4 - 64*K1**3*K3 + 640*K1**2*K2**3 + 224*K1**2*K2**2*K4 - 3296*K1**2*K2**2 - 832*K1**2*K2*K4 + 4488*K1**2*K2 - 192*K1**2*K4**2 - 4488*K1**2 + 384*K1*K2**3*K3 - 928*K1*K2**2*K3 - 128*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 4952*K1*K2*K3 + 1288*K1*K3*K4 + 344*K1*K4*K5 - 888*K2**4 - 448*K2**2*K3**2 - 72*K2**2*K4**2 + 1728*K2**2*K4 - 3326*K2**2 + 368*K2*K3*K5 + 40*K2*K4*K6 - 1800*K3**2 - 978*K4**2 - 160*K5**2 - 2*K6**2 + 3496 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.217'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4226', 'vk6.4305', 'vk6.5491', 'vk6.5603', 'vk6.7590', 'vk6.7683', 'vk6.9091', 'vk6.9170', 'vk6.18382', 'vk6.18722', 'vk6.24839', 'vk6.25298', 'vk6.37027', 'vk6.37477', 'vk6.44192', 'vk6.44513', 'vk6.48546', 'vk6.48601', 'vk6.49247', 'vk6.49361', 'vk6.50333', 'vk6.50390', 'vk6.51072', 'vk6.51103', 'vk6.56155', 'vk6.56384', 'vk6.60684', 'vk6.61035', 'vk6.65819', 'vk6.66073', 'vk6.68812', 'vk6.69022'] |
| 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 | O1O2O3O4O5U2O6U5U6U1U4U3 |
| R3 orbit | {'O1O2O3O4O5U2O6U5U6U1U4U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U3U2U5U6U1O6U4 |
| Gauss code of K* | O1O2O3O4O5U3U6U5U4U1O6U2 |
| Gauss code of -K* | O1O2O3O4O5U4O6U5U2U1U6U3 |
| 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 -3 2 2 0 1],[ 2 0 -1 3 2 0 1],[ 3 1 0 3 2 1 1],[-2 -3 -3 0 0 -1 1],[-2 -2 -2 0 0 -1 1],[ 0 0 -1 1 1 0 1],[-1 -1 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 0 1 -1 -2 -2],[-2 0 0 1 -1 -3 -3],[-1 -1 -1 0 -1 -1 -1],[ 0 1 1 1 0 0 -1],[ 2 2 3 1 0 0 -1],[ 3 2 3 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,0,-1,1,2,2,-1,1,3,3,1,1,1,0,1,1] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,2,3,2,3,2,2,1,2,0,1,1,2,2,0] |
| Phi of -K | [-3,-2,0,1,2,2,0,2,3,2,3,2,2,1,2,0,1,1,2,2,0] |
| Phi of K* | [-2,-2,-1,0,2,3,0,2,1,1,2,2,1,2,3,0,2,3,2,2,0] |
| Phi of -K* | [-3,-2,0,1,2,2,1,1,1,2,3,0,1,2,3,1,1,1,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 7z^2+24z+21 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2-4w^3z+28w^2z+21w |
| Inner characteristic polynomial | t^6+35t^4+17t^2+1 |
| Outer characteristic polynomial | t^7+57t^5+68t^3+13t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | 96*K1**4*K2 - 128*K1**4 - 64*K1**3*K3 + 640*K1**2*K2**3 + 224*K1**2*K2**2*K4 - 3296*K1**2*K2**2 - 832*K1**2*K2*K4 + 4488*K1**2*K2 - 192*K1**2*K4**2 - 4488*K1**2 + 384*K1*K2**3*K3 - 928*K1*K2**2*K3 - 128*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 4952*K1*K2*K3 + 1288*K1*K3*K4 + 344*K1*K4*K5 - 888*K2**4 - 448*K2**2*K3**2 - 72*K2**2*K4**2 + 1728*K2**2*K4 - 3326*K2**2 + 368*K2*K3*K5 + 40*K2*K4*K6 - 1800*K3**2 - 978*K4**2 - 160*K5**2 - 2*K6**2 + 3496 |
| 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 |