| Min(phi) over symmetries of the knot is: [-3,-2,1,1,1,2,0,2,3,3,2,1,2,2,2,0,0,1,0,2,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.340'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1*K2 - 2*K1 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.233', '6.340', '6.382', '6.550', '6.656', '6.663', '6.683', '6.698', '6.739', '6.745', '6.759', '6.765', '6.1357', '6.1358', '6.1370'] |
| Outer characteristic polynomial of the knot is: t^7+68t^5+48t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.340'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**2*K2**4 + 288*K1**2*K2**3 - 1808*K1**2*K2**2 + 1504*K1**2*K2 - 848*K1**2 + 128*K1*K2**3*K3 + 1088*K1*K2*K3 - 32*K2**6 + 32*K2**4*K4 - 448*K2**4 - 16*K2**2*K3**2 - 8*K2**2*K4**2 + 248*K2**2*K4 - 288*K2**2 - 144*K3**2 - 40*K4**2 + 534 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.340'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17006', 'vk6.17247', 'vk6.17541', 'vk6.17549', 'vk6.17596', 'vk6.17604', 'vk6.21917', 'vk6.24049', 'vk6.24059', 'vk6.24151', 'vk6.27972', 'vk6.29445', 'vk6.35482', 'vk6.35931', 'vk6.36325', 'vk6.36337', 'vk6.36402', 'vk6.39376', 'vk6.41561', 'vk6.43450', 'vk6.43458', 'vk6.43502', 'vk6.45946', 'vk6.47628', 'vk6.55181', 'vk6.55423', 'vk6.55631', 'vk6.55639', 'vk6.55662', 'vk6.58566', 'vk6.60149', 'vk6.60212', 'vk6.62055', 'vk6.63046', 'vk6.64979', 'vk6.65187', 'vk6.65332', 'vk6.65371', 'vk6.68502', 'vk6.68529'] |
| 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 | O1O2O3O4O5U3U1O6U5U4U6U2 |
| R3 orbit | {'O1O2O3O4O5U3U1O6U5U4U6U2', 'O1O2O3O4U5U1O6U4U3U6O5U2'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U4U6U2U1O6U5U3 |
| Gauss code of K* | O1O2O3O4U5U4U6U2U1O6O5U3 |
| Gauss code of -K* | O1O2O3O4U2O5O6U4U3U6U1U5 |
| 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 -3 1 -2 1 1 2],[ 3 0 3 0 3 2 2],[-1 -3 0 -2 0 0 2],[ 2 0 2 0 2 1 2],[-1 -3 0 -2 0 0 2],[-1 -2 0 -1 0 0 1],[-2 -2 -2 -2 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 1 -2 -3],[-2 0 -1 -2 -2 -2 -2],[-1 1 0 0 0 -1 -2],[-1 2 0 0 0 -2 -3],[-1 2 0 0 0 -2 -3],[ 2 2 1 2 2 0 0],[ 3 2 2 3 3 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,-1,2,3,1,2,2,2,2,0,0,1,2,0,2,3,2,3,0] |
| Phi over symmetry | [-3,-2,1,1,1,2,0,2,3,3,2,1,2,2,2,0,0,1,0,2,2] |
| Phi of -K | [-3,-2,1,1,1,2,1,1,1,2,3,1,1,2,2,0,0,-1,0,-1,0] |
| Phi of K* | [-2,-1,-1,-1,2,3,-1,-1,0,2,3,0,0,1,1,0,1,1,2,2,1] |
| Phi of -K* | [-3,-2,1,1,1,2,0,2,3,3,2,1,2,2,2,0,0,1,0,2,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-3t |
| Normalized Jones-Krushkal polynomial | z+3 |
| Enhanced Jones-Krushkal polynomial | -12w^3z+13w^2z+3w |
| Inner characteristic polynomial | t^6+48t^4+16t^2 |
| Outer characteristic polynomial | t^7+68t^5+48t^3 |
| Flat arrow polynomial | 4*K1**3 - 2*K1*K2 - 2*K1 + 1 |
| 2-strand cable arrow polynomial | -192*K1**2*K2**4 + 288*K1**2*K2**3 - 1808*K1**2*K2**2 + 1504*K1**2*K2 - 848*K1**2 + 128*K1*K2**3*K3 + 1088*K1*K2*K3 - 32*K2**6 + 32*K2**4*K4 - 448*K2**4 - 16*K2**2*K3**2 - 8*K2**2*K4**2 + 248*K2**2*K4 - 288*K2**2 - 144*K3**2 - 40*K4**2 + 534 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{4, 6}, {1, 5}, {2, 3}]] |
| If K is slice | False |