| Min(phi) over symmetries of the knot is: [0,0,0,0,-1,0,0,0,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.2084', '7.45422'] |
| Arrow polynomial of the knot is: -16*K1**2 + 8*K2 + 9 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.1244', '6.1401', '6.2079', '6.2084'] |
| Outer characteristic polynomial of the knot is: t^5+2t^3+t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.2084', '7.45422'] |
| 2-strand cable arrow polynomial of the knot is: 1408*K1**4*K2 - 6336*K1**4 - 640*K1**3*K3 + 256*K1**2*K2**3 - 6912*K1**2*K2**2 - 256*K1**2*K2*K4 + 14336*K1**2*K2 - 6992*K1**2 - 512*K1*K2**2*K3 + 7104*K1*K2*K3 + 384*K1*K3*K4 - 704*K2**4 + 1088*K2**2*K4 - 6032*K2**2 - 1840*K3**2 - 400*K4**2 + 6046 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2084'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.72425', 'vk6.72477', 'vk6.72836', 'vk6.72898', 'vk6.74458', 'vk6.75071', 'vk6.76967', 'vk6.77786', 'vk6.77975', 'vk6.79465', 'vk6.79914', 'vk6.80934', 'vk6.87228', 'vk6.89367'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is a. |
| The fillings (up to the first 10) associated to the algebraic genus: |
| Or click here to check the fillings |
| invariant | value |
|---|---|
| Gauss code | O1O2U3U1O4O3U5U2O6O5U4U6 |
| R3 orbit | {'O1O2U3U1O4O3U5U2O6O5U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | Same |
| Gauss code of K* | Same |
| Gauss code of -K* | Same |
| Diagrammatic symmetry type | a |
| 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 1 0 -1 0 0],[ 0 0 0 0 0 -1 0],[-1 0 0 -1 -1 -1 0],[ 0 0 1 0 -1 0 -1],[ 1 0 1 1 0 1 0],[ 0 1 1 0 -1 0 0],[ 0 0 0 1 0 0 0]] |
| Primitive based matrix | [[ 0 0 0 0 0],[ 0 0 1 0 0],[ 0 -1 0 0 0],[ 0 0 0 0 1],[ 0 0 0 -1 0]] |
| If based matrix primitive | False |
| Phi of primitive based matrix | [0,0,0,0,-1,0,0,0,0,-1] |
| Phi over symmetry | [0,0,0,0,-1,0,0,0,0,-1] |
| Phi of -K | [0,0,0,0,-1,0,0,0,0,-1] |
| Phi of K* | [0,0,0,0,-1,0,0,0,0,-1] |
| Phi of -K* | [0,0,0,0,-1,0,0,0,0,-1] |
| Symmetry type of based matrix | a |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 2z^2+23z+39 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+23w^2z+39w |
| Inner characteristic polynomial | t^4+2t^2+1 |
| Outer characteristic polynomial | t^5+2t^3+t |
| Flat arrow polynomial | -16*K1**2 + 8*K2 + 9 |
| 2-strand cable arrow polynomial | 1408*K1**4*K2 - 6336*K1**4 - 640*K1**3*K3 + 256*K1**2*K2**3 - 6912*K1**2*K2**2 - 256*K1**2*K2*K4 + 14336*K1**2*K2 - 6992*K1**2 - 512*K1*K2**2*K3 + 7104*K1*K2*K3 + 384*K1*K3*K4 - 704*K2**4 + 1088*K2**2*K4 - 6032*K2**2 - 1840*K3**2 - 400*K4**2 + 6046 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{3, 6}, {1, 5}, {2, 4}]] |
| If K is slice | True |