| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,0,2,2,4,2,0,2,1,-1,1,1,1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1821'] |
| Arrow polynomial of the knot is: 4*K1**3 - 8*K1**2 - 4*K1*K2 - K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.315', '6.337', '6.389', '6.418', '6.599', '6.675', '6.686', '6.688', '6.746', '6.747', '6.809', '6.1034', '6.1128', '6.1133', '6.1334', '6.1363', '6.1489', '6.1539', '6.1564', '6.1821', '6.1863'] |
| Outer characteristic polynomial of the knot is: t^7+25t^5+96t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1821'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 512*K1**4*K2 - 960*K1**4 + 416*K1**2*K2**3 - 1984*K1**2*K2**2 + 2408*K1**2*K2 - 64*K1**2*K3**2 - 1688*K1**2 + 160*K1*K2**3*K3 + 2048*K1*K2*K3 + 256*K1*K3*K4 - 32*K2**6 + 64*K2**4*K4 - 592*K2**4 - 352*K2**2*K3**2 - 48*K2**2*K4**2 + 432*K2**2*K4 - 1190*K2**2 + 200*K2*K3*K5 + 16*K2*K4*K6 - 728*K3**2 - 244*K4**2 - 32*K5**2 - 2*K6**2 + 1594 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1821'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4747', 'vk6.5076', 'vk6.6289', 'vk6.6730', 'vk6.8254', 'vk6.8705', 'vk6.9640', 'vk6.9957', 'vk6.20402', 'vk6.21755', 'vk6.27744', 'vk6.29278', 'vk6.39176', 'vk6.41408', 'vk6.45908', 'vk6.47545', 'vk6.48779', 'vk6.48992', 'vk6.49591', 'vk6.49796', 'vk6.50795', 'vk6.51012', 'vk6.51282', 'vk6.51479', 'vk6.57271', 'vk6.58500', 'vk6.61927', 'vk6.63024', 'vk6.66884', 'vk6.67766', 'vk6.69520', 'vk6.70230'] |
| 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 | O1O2O3U1U2O4U3O5O6U5U4U6 |
| R3 orbit | {'O1O2O3U1U2O4U3O5O6U5U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U6O4O6U1O5U2U3 |
| Gauss code of K* | O1O2O3U4U5U6O4O5U2O6U1U3 |
| Gauss code of -K* | O1O2O3U1U3O4U2O5O6U4U5U6 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 0 1 0 -1 2],[ 2 0 1 2 1 0 0],[ 0 -1 0 1 1 0 0],[-1 -2 -1 0 1 0 1],[ 0 -1 -1 -1 0 0 2],[ 1 0 0 0 0 0 1],[-2 0 0 -1 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 0 -2 -1 0],[-1 1 0 -1 1 0 -2],[ 0 0 1 0 1 0 -1],[ 0 2 -1 -1 0 0 -1],[ 1 1 0 0 0 0 0],[ 2 0 2 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,0,2,1,0,1,-1,0,2,-1,0,1,0,1,0] |
| Phi over symmetry | [-2,-1,0,0,1,2,0,0,2,2,4,2,0,2,1,-1,1,1,1,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,1,1,1,1,4,1,1,2,2,-1,0,2,2,0,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,0,2,2,4,2,0,2,1,-1,1,1,1,1,1] |
| Phi of -K* | [-2,-1,0,0,1,2,0,1,1,2,0,0,0,0,1,-1,-1,2,1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 11z+23 |
| Enhanced Jones-Krushkal polynomial | -2w^3z+13w^2z+23w |
| Inner characteristic polynomial | t^6+15t^4+24t^2 |
| Outer characteristic polynomial | t^7+25t^5+96t^3 |
| Flat arrow polynomial | 4*K1**3 - 8*K1**2 - 4*K1*K2 - K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 512*K1**4*K2 - 960*K1**4 + 416*K1**2*K2**3 - 1984*K1**2*K2**2 + 2408*K1**2*K2 - 64*K1**2*K3**2 - 1688*K1**2 + 160*K1*K2**3*K3 + 2048*K1*K2*K3 + 256*K1*K3*K4 - 32*K2**6 + 64*K2**4*K4 - 592*K2**4 - 352*K2**2*K3**2 - 48*K2**2*K4**2 + 432*K2**2*K4 - 1190*K2**2 + 200*K2*K3*K5 + 16*K2*K4*K6 - 728*K3**2 - 244*K4**2 - 32*K5**2 - 2*K6**2 + 1594 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}]] |
| If K is slice | True |