| Min(phi) over symmetries of the knot is: [-1,-1,0,0,1,1,-1,-1,0,1,2,1,1,0,0,0,1,0,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.2001'] |
| 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+14t^5+31t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.2001'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 - 320*K1**4*K2**2 + 3264*K1**4*K2 - 5840*K1**4 + 160*K1**3*K2*K3 - 992*K1**3*K3 + 1952*K1**2*K2**3 - 9888*K1**2*K2**2 - 384*K1**2*K2*K4 + 12176*K1**2*K2 - 112*K1**2*K3**2 - 4780*K1**2 - 1888*K1*K2**2*K3 + 7792*K1*K2*K3 + 504*K1*K3*K4 - 1536*K2**4 + 1656*K2**2*K4 - 4296*K2**2 - 1580*K3**2 - 344*K4**2 + 4518 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2001'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13881', 'vk6.13978', 'vk6.14133', 'vk6.14356', 'vk6.14952', 'vk6.15075', 'vk6.15589', 'vk6.16059', 'vk6.16283', 'vk6.16308', 'vk6.17415', 'vk6.22598', 'vk6.22631', 'vk6.23927', 'vk6.33700', 'vk6.33777', 'vk6.34146', 'vk6.34260', 'vk6.34586', 'vk6.36194', 'vk6.36219', 'vk6.42284', 'vk6.53867', 'vk6.53910', 'vk6.54106', 'vk6.54412', 'vk6.54570', 'vk6.55574', 'vk6.59023', 'vk6.59042', 'vk6.60069', 'vk6.64570'] |
| 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 | O1O2U1O3U4O5U3U2O4O6U5U6 |
| R3 orbit | {'O1O2U1O3U4O5U3U2O4O6U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2U3U4O3O5U1U6O4U5O6U2 |
| Gauss code of K* | O1O2U3U4O5O4U6U2O6U1O3U5 |
| Gauss code of -K* | O1O2U3O4U2O5U1U5O6O3U6U4 |
| 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 0 1],[ 1 0 1 0 0 1 0],[-1 -1 0 0 -2 1 1],[ 0 0 0 0 0 0 1],[ 1 0 2 0 0 0 0],[ 0 -1 -1 0 0 0 1],[-1 0 -1 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 -1 -1],[-1 0 1 1 0 -1 -2],[-1 -1 0 -1 -1 0 0],[ 0 -1 1 0 0 -1 0],[ 0 0 1 0 0 0 0],[ 1 1 0 1 0 0 0],[ 1 2 0 0 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,1,1,-1,-1,0,1,2,1,1,0,0,0,1,0,0,0,0] |
| Phi over symmetry | [-1,-1,0,0,1,1,-1,-1,0,1,2,1,1,0,0,0,1,0,0,0,0] |
| Phi of -K | [-1,-1,0,0,1,1,0,0,1,1,2,1,1,0,2,0,2,0,1,0,-1] |
| Phi of K* | [-1,-1,0,0,1,1,-1,0,0,2,2,1,2,0,1,0,1,1,1,0,0] |
| Phi of -K* | [-1,-1,0,0,1,1,0,0,0,0,2,0,1,0,1,0,1,0,1,-1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 4z^2+25z+35 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+25w^2z+35w |
| Inner characteristic polynomial | t^6+10t^4+15t^2+4 |
| Outer characteristic polynomial | t^7+14t^5+31t^3+11t |
| Flat arrow polynomial | -12*K1**2 + 6*K2 + 7 |
| 2-strand cable arrow polynomial | -64*K1**6 - 320*K1**4*K2**2 + 3264*K1**4*K2 - 5840*K1**4 + 160*K1**3*K2*K3 - 992*K1**3*K3 + 1952*K1**2*K2**3 - 9888*K1**2*K2**2 - 384*K1**2*K2*K4 + 12176*K1**2*K2 - 112*K1**2*K3**2 - 4780*K1**2 - 1888*K1*K2**2*K3 + 7792*K1*K2*K3 + 504*K1*K3*K4 - 1536*K2**4 + 1656*K2**2*K4 - 4296*K2**2 - 1580*K3**2 - 344*K4**2 + 4518 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{2, 6}, {3, 5}, {1, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}], [{4, 6}, {3, 5}, {1, 2}]] |
| If K is slice | False |