| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,0,0,2,3,1,1,1,1,-1,0,1,1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.805'] |
| Arrow polynomial of the knot is: -12*K1**2 - 4*K1*K2 + 2*K1 + 6*K2 + 2*K3 + 7 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.546', '6.591', '6.598', '6.666', '6.680', '6.742', '6.778', '6.805', '6.822', '6.824', '6.1129', '6.1512', '6.1647', '6.1678', '6.1705', '6.1847', '6.1857'] |
| Outer characteristic polynomial of the knot is: t^7+33t^5+72t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.805'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**6 - 128*K1**4*K2**2 + 1312*K1**4*K2 - 4672*K1**4 + 512*K1**3*K2*K3 + 32*K1**3*K3*K4 - 960*K1**3*K3 - 4976*K1**2*K2**2 - 448*K1**2*K2*K4 + 10504*K1**2*K2 - 768*K1**2*K3**2 - 80*K1**2*K4**2 - 5620*K1**2 - 960*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 7512*K1*K2*K3 + 1480*K1*K3*K4 + 152*K1*K4*K5 - 272*K2**4 - 192*K2**2*K3**2 - 16*K2**2*K4**2 + 1064*K2**2*K4 - 5284*K2**2 + 304*K2*K3*K5 + 32*K2*K4*K6 - 2488*K3**2 - 740*K4**2 - 132*K5**2 - 12*K6**2 + 5226 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.805'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4774', 'vk6.4780', 'vk6.5109', 'vk6.5115', 'vk6.6340', 'vk6.6767', 'vk6.6777', 'vk6.8293', 'vk6.8299', 'vk6.8744', 'vk6.9663', 'vk6.9673', 'vk6.9972', 'vk6.9982', 'vk6.21024', 'vk6.21028', 'vk6.22446', 'vk6.22450', 'vk6.28471', 'vk6.40244', 'vk6.40256', 'vk6.42170', 'vk6.46742', 'vk6.46754', 'vk6.48804', 'vk6.49019', 'vk6.49029', 'vk6.49839', 'vk6.49845', 'vk6.51498', 'vk6.58971', 'vk6.69809'] |
| 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 | O1O2O3O4U5O6U4U6U2O5U1U3 |
| R3 orbit | {'O1O2O3O4U5O6U4U6U2O5U1U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U4O5U3U6U1O6U5 |
| Gauss code of K* | O1O2O3U4O5O6U5U3U6U1O4U2 |
| Gauss code of -K* | O1O2O3U2O4U3U5U1U6O5O6U4 |
| 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 0 2 0 -2 1],[ 1 0 1 2 0 -1 1],[ 0 -1 0 0 -1 -1 1],[-2 -2 0 0 0 -3 1],[ 0 0 1 0 0 -1 1],[ 2 1 1 3 1 0 1],[-1 -1 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 1 0 0 -2 -3],[-1 -1 0 -1 -1 -1 -1],[ 0 0 1 0 1 0 -1],[ 0 0 1 -1 0 -1 -1],[ 1 2 1 0 1 0 -1],[ 2 3 1 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,-1,0,0,2,3,1,1,1,1,-1,0,1,1,1,1] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,0,0,2,3,1,1,1,1,-1,0,1,1,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,0,1,1,2,1,0,1,1,1,1,0,2,0,2,2] |
| Phi of K* | [-2,-1,0,0,1,2,2,2,2,1,1,0,0,1,2,-1,0,1,1,1,0] |
| Phi of -K* | [-2,-1,0,0,1,2,1,1,1,1,3,0,1,1,2,1,1,0,1,0,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 19z+39 |
| Enhanced Jones-Krushkal polynomial | 19w^2z+39w |
| Inner characteristic polynomial | t^6+23t^4+34t^2+4 |
| Outer characteristic polynomial | t^7+33t^5+72t^3+9t |
| Flat arrow polynomial | -12*K1**2 - 4*K1*K2 + 2*K1 + 6*K2 + 2*K3 + 7 |
| 2-strand cable arrow polynomial | -256*K1**6 - 128*K1**4*K2**2 + 1312*K1**4*K2 - 4672*K1**4 + 512*K1**3*K2*K3 + 32*K1**3*K3*K4 - 960*K1**3*K3 - 4976*K1**2*K2**2 - 448*K1**2*K2*K4 + 10504*K1**2*K2 - 768*K1**2*K3**2 - 80*K1**2*K4**2 - 5620*K1**2 - 960*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 7512*K1*K2*K3 + 1480*K1*K3*K4 + 152*K1*K4*K5 - 272*K2**4 - 192*K2**2*K3**2 - 16*K2**2*K4**2 + 1064*K2**2*K4 - 5284*K2**2 + 304*K2*K3*K5 + 32*K2*K4*K6 - 2488*K3**2 - 740*K4**2 - 132*K5**2 - 12*K6**2 + 5226 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}]] |
| If K is slice | False |