| Min(phi) over symmetries of the knot is: [-1,0,0,0,0,1,-1,0,1,1,0,-1,-1,0,1,-1,-1,1,-1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.2016'] |
| Arrow polynomial of the knot is: -12*K1**2 + 6*K2 + 7 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.612', '6.1246', '6.1402', '6.1410', '6.1411', '6.1468', '6.1617', '6.1666', '6.1667', '6.1815', '6.1904', '6.1994', '6.1995', '6.1996', '6.2001', '6.2014', '6.2015', '6.2016', '6.2017', '6.2020', '6.2022'] |
| Outer characteristic polynomial of the knot is: t^7+13t^5+28t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.2016'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 256*K1**4*K2 - 1952*K1**4 + 192*K1**3*K2*K3 - 160*K1**3*K3 - 2464*K1**2*K2**2 - 96*K1**2*K2*K4 + 4752*K1**2*K2 - 96*K1**2*K3**2 - 2256*K1**2 + 2368*K1*K2*K3 + 80*K1*K3*K4 - 176*K2**4 + 160*K2**2*K4 - 1824*K2**2 - 560*K3**2 - 48*K4**2 + 1886 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2016'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16499', 'vk6.16592', 'vk6.18094', 'vk6.18432', 'vk6.22930', 'vk6.23027', 'vk6.23488', 'vk6.23827', 'vk6.24541', 'vk6.24960', 'vk6.35016', 'vk6.35637', 'vk6.36684', 'vk6.37108', 'vk6.39461', 'vk6.41662', 'vk6.42476', 'vk6.42589', 'vk6.43960', 'vk6.44277', 'vk6.46045', 'vk6.47713', 'vk6.54726', 'vk6.54823', 'vk6.56212', 'vk6.57467', 'vk6.59190', 'vk6.59255', 'vk6.59638', 'vk6.59986', 'vk6.60807', 'vk6.62138', 'vk6.64805', 'vk6.65038', 'vk6.65568', 'vk6.65880', 'vk6.68042', 'vk6.68107', 'vk6.68646', 'vk6.68861'] |
| 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 | O1O2U3O4U2O5U4U1O3O6U5U6 |
| R3 orbit | {'O1O2U3U1O4O5U2U4O3O6U5U6', 'O1O2U3O4U2O5U4U1O3O6U5U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2U3U4O3O5U2U6O4U1O6U5 |
| Gauss code of K* | O1O2U3U4O5O4U2U6O3U1O6U5 |
| Gauss code of -K* | O1O2U3O4U2O5U4U1O6O3U6U5 |
| 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 0 0 -1 0 0 1],[ 0 0 -1 -1 1 1 1],[ 0 1 0 -1 1 0 0],[ 1 1 1 0 0 -1 0],[ 0 -1 -1 0 0 1 1],[ 0 -1 0 1 -1 0 1],[-1 -1 0 0 -1 -1 0]] |
| Primitive based matrix | [[ 0 1 0 0 0 0 -1],[-1 0 0 -1 -1 -1 0],[ 0 0 0 1 1 0 -1],[ 0 1 -1 0 1 1 -1],[ 0 1 -1 -1 0 1 0],[ 0 1 0 -1 -1 0 1],[ 1 0 1 1 0 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,0,0,0,0,1,0,1,1,1,0,-1,-1,0,1,-1,-1,1,-1,0,-1] |
| Phi over symmetry | [-1,0,0,0,0,1,-1,0,1,1,0,-1,-1,0,1,-1,-1,1,-1,1,0] |
| Phi of -K | [-1,0,0,0,0,1,0,0,1,2,2,-1,-1,0,1,-1,-1,0,-1,0,0] |
| Phi of K* | [-1,0,0,0,0,1,0,0,0,1,2,-1,-1,0,2,-1,-1,1,-1,0,0] |
| Phi of -K* | [-1,0,0,0,0,1,-1,0,1,1,0,-1,-1,0,1,-1,-1,1,-1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 13z+27 |
| Enhanced Jones-Krushkal polynomial | 13w^2z+27w |
| Inner characteristic polynomial | t^6+11t^4+12t^2 |
| Outer characteristic polynomial | t^7+13t^5+28t^3+3t |
| Flat arrow polynomial | -12*K1**2 + 6*K2 + 7 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 256*K1**4*K2 - 1952*K1**4 + 192*K1**3*K2*K3 - 160*K1**3*K3 - 2464*K1**2*K2**2 - 96*K1**2*K2*K4 + 4752*K1**2*K2 - 96*K1**2*K3**2 - 2256*K1**2 + 2368*K1*K2*K3 + 80*K1*K3*K4 - 176*K2**4 + 160*K2**2*K4 - 1824*K2**2 - 560*K3**2 - 48*K4**2 + 1886 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {5}, {2, 4}, {1}]] |
| If K is slice | False |