| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,1,1,1,1,0,1,1,1,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1745'] |
| Arrow polynomial of the knot is: -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.239', '6.428', '6.470', '6.556', '6.700', '6.910', '6.962', '6.1006', '6.1013', '6.1038', '6.1207', '6.1224', '6.1225', '6.1269', '6.1270', '6.1308', '6.1319', '6.1320', '6.1323', '6.1485', '6.1551', '6.1579', '6.1581', '6.1660', '6.1672', '6.1679', '6.1711', '6.1719', '6.1732', '6.1745', '6.1748', '6.1827', '6.1836', '6.1838', '6.1850', '6.1866'] |
| Outer characteristic polynomial of the knot is: t^7+26t^5+33t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1745'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 384*K1**4*K2 - 3808*K1**4 + 1056*K1**3*K2*K3 + 192*K1**3*K3*K4 - 672*K1**3*K3 - 2624*K1**2*K2**2 - 736*K1**2*K2*K4 + 6096*K1**2*K2 - 2048*K1**2*K3**2 - 96*K1**2*K3*K5 - 336*K1**2*K4**2 - 3128*K1**2 - 224*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 5384*K1*K2*K3 + 2600*K1*K3*K4 + 392*K1*K4*K5 - 24*K2**4 - 32*K2**2*K3**2 - 16*K2**2*K4**2 + 304*K2**2*K4 - 2932*K2**2 + 104*K2*K3*K5 + 32*K2*K4*K6 - 2124*K3**2 - 854*K4**2 - 124*K5**2 - 12*K6**2 + 3500 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1745'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4829', 'vk6.5173', 'vk6.6392', 'vk6.6823', 'vk6.8361', 'vk6.8791', 'vk6.9727', 'vk6.10031', 'vk6.11612', 'vk6.11965', 'vk6.12954', 'vk6.20459', 'vk6.20732', 'vk6.21812', 'vk6.27847', 'vk6.29355', 'vk6.31423', 'vk6.32597', 'vk6.39277', 'vk6.39772', 'vk6.41455', 'vk6.46336', 'vk6.47582', 'vk6.47911', 'vk6.49067', 'vk6.49897', 'vk6.51325', 'vk6.51543', 'vk6.53219', 'vk6.57318', 'vk6.62008', 'vk6.64308'] |
| 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 | O1O2O3U4U2O4O5U1U3O6U5U6 |
| R3 orbit | {'O1O2O3U4U2O4O5U1U3O6U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O4U1U3O5O6U2U6 |
| Gauss code of K* | O1O2U3O4O3U1U5U2O6O5U6U4 |
| Gauss code of -K* | O1O2U1O3O4U2U5O6O5U3U6U4 |
| 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 0 1 -1 1 1],[ 2 0 1 2 1 2 1],[ 0 -1 0 0 0 1 0],[-1 -2 0 0 -1 1 1],[ 1 -1 0 1 0 1 1],[-1 -2 -1 -1 -1 0 1],[-1 -1 0 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 1 0 -1 -2],[-1 -1 0 1 -1 -1 -2],[-1 -1 -1 0 0 -1 -1],[ 0 0 1 0 0 0 -1],[ 1 1 1 1 0 0 -1],[ 2 2 2 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,-1,0,1,2,-1,1,1,2,0,1,1,0,1,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,1,1,1,1,0,1,1,1,-1,-1] |
| Phi of -K | [-2,-1,0,1,1,1,0,1,1,1,2,1,1,1,1,0,1,1,1,-1,-1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,-1,1,1,2,-1,0,1,1,1,1,1,1,1,0] |
| Phi of -K* | [-2,-1,0,1,1,1,1,1,1,2,2,0,1,1,1,0,0,1,-1,-1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+18t^4+14t^2+1 |
| Outer characteristic polynomial | t^7+26t^5+33t^3+8t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -128*K1**6 + 384*K1**4*K2 - 3808*K1**4 + 1056*K1**3*K2*K3 + 192*K1**3*K3*K4 - 672*K1**3*K3 - 2624*K1**2*K2**2 - 736*K1**2*K2*K4 + 6096*K1**2*K2 - 2048*K1**2*K3**2 - 96*K1**2*K3*K5 - 336*K1**2*K4**2 - 3128*K1**2 - 224*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 5384*K1*K2*K3 + 2600*K1*K3*K4 + 392*K1*K4*K5 - 24*K2**4 - 32*K2**2*K3**2 - 16*K2**2*K4**2 + 304*K2**2*K4 - 2932*K2**2 + 104*K2*K3*K5 + 32*K2*K4*K6 - 2124*K3**2 - 854*K4**2 - 124*K5**2 - 12*K6**2 + 3500 |
| 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 |