| Min(phi) over symmetries of the knot is: [-1,-1,0,0,1,1,-1,0,0,1,1,0,1,1,2,1,0,1,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1666'] |
| 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+18t^5+24t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1666', '7.44874'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 864*K1**4*K2 - 2336*K1**4 + 256*K1**3*K2*K3 - 352*K1**3*K3 + 128*K1**2*K2**3 - 3008*K1**2*K2**2 - 128*K1**2*K2*K4 + 4712*K1**2*K2 - 192*K1**2*K3**2 - 2000*K1**2 - 64*K1*K2**2*K3 + 2776*K1*K2*K3 + 192*K1*K3*K4 - 144*K2**4 + 128*K2**2*K4 - 1760*K2**2 - 656*K3**2 - 64*K4**2 + 1838 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1666'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4430', 'vk6.4525', 'vk6.4844', 'vk6.5188', 'vk6.5812', 'vk6.5939', 'vk6.6411', 'vk6.6428', 'vk6.6844', 'vk6.7980', 'vk6.8372', 'vk6.8389', 'vk6.8800', 'vk6.9291', 'vk6.9410', 'vk6.9736', 'vk6.17886', 'vk6.17951', 'vk6.18280', 'vk6.18615', 'vk6.24389', 'vk6.25170', 'vk6.30037', 'vk6.30100', 'vk6.36890', 'vk6.37348', 'vk6.39824', 'vk6.39844', 'vk6.43824', 'vk6.44111', 'vk6.44434', 'vk6.46387', 'vk6.46406', 'vk6.47963', 'vk6.47983', 'vk6.48633', 'vk6.49082', 'vk6.49917', 'vk6.50617', 'vk6.51137'] |
| 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 | O1O2O3U2O4U3U1U5O6O5U4U6 |
| R3 orbit | {'O1O2U1O3O4U2U3U5O6O5U4U6', 'O1O2O3U2O4U3U1U5O6O5U4U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3U4U5O6O4U6U3U1O5U2 |
| Gauss code of K* | O1O2O3U4U3O5O4U2U6U1O6U5 |
| Gauss code of -K* | O1O2O3U4O5U3U5U2O6O4U1U6 |
| 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 -1 -1 0 1 1 0],[ 1 0 -1 1 2 1 1],[ 1 1 0 1 1 1 0],[ 0 -1 -1 0 1 0 1],[-1 -2 -1 -1 0 -1 0],[-1 -1 -1 0 1 0 0],[ 0 -1 0 -1 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 -1 -1],[-1 0 1 0 0 -1 -1],[-1 -1 0 0 -1 -1 -2],[ 0 0 0 0 -1 0 -1],[ 0 0 1 1 0 -1 -1],[ 1 1 1 0 1 0 1],[ 1 1 2 1 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,1,1,-1,0,0,1,1,0,1,1,2,1,0,1,1,1,-1] |
| Phi over symmetry | [-1,-1,0,0,1,1,-1,0,0,1,1,0,1,1,2,1,0,1,1,1,-1] |
| Phi of -K | [-1,-1,0,0,1,1,-1,0,1,1,1,0,0,0,1,-1,0,1,1,1,1] |
| Phi of K* | [-1,-1,0,0,1,1,-1,0,1,0,1,1,1,1,1,1,0,0,0,1,-1] |
| Phi of -K* | [-1,-1,0,0,1,1,-1,1,1,1,2,0,1,1,1,-1,0,0,0,1,1] |
| 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+14t^4+8t^2 |
| Outer characteristic polynomial | t^7+18t^5+24t^3+3t |
| Flat arrow polynomial | -12*K1**2 + 6*K2 + 7 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 864*K1**4*K2 - 2336*K1**4 + 256*K1**3*K2*K3 - 352*K1**3*K3 + 128*K1**2*K2**3 - 3008*K1**2*K2**2 - 128*K1**2*K2*K4 + 4712*K1**2*K2 - 192*K1**2*K3**2 - 2000*K1**2 - 64*K1*K2**2*K3 + 2776*K1*K2*K3 + 192*K1*K3*K4 - 144*K2**4 + 128*K2**2*K4 - 1760*K2**2 - 656*K3**2 - 64*K4**2 + 1838 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}]] |
| If K is slice | False |