| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,-1,-1,1,2,3,1,0,0,0,1,1,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1047'] |
| Arrow polynomial of the knot is: -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.120', '6.213', '6.216', '6.320', '6.322', '6.615', '6.617', '6.891', '6.951', '6.955', '6.1001', '6.1012', '6.1022', '6.1043', '6.1047', '6.1063', '6.1074', '6.1249', '6.1544', '6.1546', '6.1555', '6.1573', '6.1574', '6.1585', '6.1756', '6.1757', '6.1762', '6.1802', '6.1803', '6.1824', '6.1881', '6.1935'] |
| Outer characteristic polynomial of the knot is: t^7+38t^5+179t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1047'] |
| 2-strand cable arrow polynomial of the knot is: -336*K1**4 + 192*K1**3*K2*K3 - 352*K1**2*K2**2 + 472*K1**2*K2 - 528*K1**2*K3**2 - 1028*K1**2 + 1856*K1*K2*K3 + 744*K1*K3*K4 + 8*K1*K4*K5 - 8*K2**4 - 16*K2**2*K3**2 - 16*K2**2*K4**2 + 136*K2**2*K4 - 1004*K2**2 + 24*K2*K3*K5 + 32*K2*K4*K6 - 1024*K3**2 - 342*K4**2 - 12*K5**2 - 12*K6**2 + 1212 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1047'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4703', 'vk6.5008', 'vk6.6201', 'vk6.6672', 'vk6.8196', 'vk6.8618', 'vk6.9572', 'vk6.9911', 'vk6.17402', 'vk6.20934', 'vk6.21087', 'vk6.22346', 'vk6.22517', 'vk6.23572', 'vk6.23911', 'vk6.28417', 'vk6.36177', 'vk6.40091', 'vk6.40337', 'vk6.42138', 'vk6.43394', 'vk6.46616', 'vk6.46799', 'vk6.48056', 'vk6.48741', 'vk6.49750', 'vk6.50749', 'vk6.51439', 'vk6.57743', 'vk6.58942', 'vk6.65299', 'vk6.69779'] |
| 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 | O1O2O3O4U5U6O5U1O6U4U3U2 |
| R3 orbit | {'O1O2O3O4U5U6O5U1O6U4U3U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U3U2U1O5U4O6U5U6 |
| Gauss code of K* | O1O2O3U4U3U2U1O5O6U5O4U6 |
| Gauss code of -K* | O1O2O3U4O5U6O4O6U3U2U1U5 |
| 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 1 1 1 -1 0],[ 2 0 2 1 0 2 3],[-1 -2 0 0 0 -2 0],[-1 -1 0 0 0 -2 0],[-1 0 0 0 0 -2 0],[ 1 -2 2 2 2 0 0],[ 0 -3 0 0 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 0 0 0 -2 0],[-1 0 0 0 0 -2 -1],[-1 0 0 0 0 -2 -2],[ 0 0 0 0 0 0 -3],[ 1 2 2 2 0 0 -2],[ 2 0 1 2 3 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,0,0,0,2,0,0,0,2,1,0,2,2,0,3,2] |
| Phi over symmetry | [-2,-1,0,1,1,1,-1,-1,1,2,3,1,0,0,0,1,1,1,0,0,0] |
| Phi of -K | [-2,-1,0,1,1,1,-1,-1,1,2,3,1,0,0,0,1,1,1,0,0,0] |
| Phi of K* | [-1,-1,-1,0,1,2,0,0,1,0,1,0,1,0,2,1,0,3,1,-1,-1] |
| Phi of -K* | [-2,-1,0,1,1,1,2,3,0,1,2,0,2,2,2,0,0,0,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z+7 |
| Enhanced Jones-Krushkal polynomial | 8w^4z-16w^3z+11w^2z+7w |
| Inner characteristic polynomial | t^6+30t^4+132t^2 |
| Outer characteristic polynomial | t^7+38t^5+179t^3 |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -336*K1**4 + 192*K1**3*K2*K3 - 352*K1**2*K2**2 + 472*K1**2*K2 - 528*K1**2*K3**2 - 1028*K1**2 + 1856*K1*K2*K3 + 744*K1*K3*K4 + 8*K1*K4*K5 - 8*K2**4 - 16*K2**2*K3**2 - 16*K2**2*K4**2 + 136*K2**2*K4 - 1004*K2**2 + 24*K2*K3*K5 + 32*K2*K4*K6 - 1024*K3**2 - 342*K4**2 - 12*K5**2 - 12*K6**2 + 1212 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{3, 6}, {2, 5}, {1, 4}], [{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |