| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,1,2,2,2,1,1,1,1,0,0,0,1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.966'] |
| Arrow polynomial of the knot is: -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.65', '6.137', '6.201', '6.203', '6.214', '6.310', '6.314', '6.332', '6.385', '6.386', '6.401', '6.516', '6.564', '6.571', '6.572', '6.578', '6.621', '6.626', '6.716', '6.773', '6.807', '6.814', '6.821', '6.940', '6.966', '6.1036', '6.1071', '6.1108', '6.1111', '6.1131', '6.1188', '6.1203', '6.1206', '6.1220', '6.1340', '6.1387', '6.1548', '6.1663', '6.1680', '6.1693', '6.1831', '6.1932'] |
| Outer characteristic polynomial of the knot is: t^7+31t^5+39t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.966'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 384*K1**4*K2 - 3200*K1**4 + 32*K1**3*K2*K3 + 32*K1**3*K3*K4 - 128*K1**3*K3 - 1584*K1**2*K2**2 - 224*K1**2*K2*K4 + 5264*K1**2*K2 - 1152*K1**2*K3**2 - 96*K1**2*K3*K5 - 144*K1**2*K4**2 - 3292*K1**2 - 320*K1*K2**2*K3 - 192*K1*K2*K3*K4 + 4304*K1*K2*K3 + 2224*K1*K3*K4 + 328*K1*K4*K5 - 48*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 472*K2**2*K4 - 3044*K2**2 + 208*K2*K3*K5 + 32*K2*K4*K6 - 2080*K3**2 - 916*K4**2 - 140*K5**2 - 4*K6**2 + 3554 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.966'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3662', 'vk6.3757', 'vk6.3948', 'vk6.4043', 'vk6.4484', 'vk6.4579', 'vk6.5870', 'vk6.5997', 'vk6.7145', 'vk6.7320', 'vk6.7411', 'vk6.7915', 'vk6.8034', 'vk6.9349', 'vk6.17914', 'vk6.18011', 'vk6.18767', 'vk6.24449', 'vk6.24892', 'vk6.25353', 'vk6.37506', 'vk6.43876', 'vk6.44239', 'vk6.44542', 'vk6.48302', 'vk6.48365', 'vk6.50083', 'vk6.50193', 'vk6.50560', 'vk6.50623', 'vk6.55859', 'vk6.60731'] |
| 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 | O1O2O3O4U5U3O6O5U6U1U4U2 |
| R3 orbit | {'O1O2O3O4U5U3O6O5U6U1U4U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U3U1U4U5O6O5U2U6 |
| Gauss code of K* | O1O2O3O4U2U4U5U3O6O5U1U6 |
| Gauss code of -K* | O1O2O3O4U5U4O6O5U2U6U1U3 |
| 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 -2 1 0 2 0 -1],[ 2 0 2 1 2 2 -1],[-1 -2 0 0 1 -1 -1],[ 0 -1 0 0 0 0 -1],[-2 -2 -1 0 0 -1 -1],[ 0 -2 1 0 1 0 -1],[ 1 1 1 1 1 1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 0 -1 -1 -2],[-1 1 0 0 -1 -1 -2],[ 0 0 0 0 0 -1 -1],[ 0 1 1 0 0 -1 -2],[ 1 1 1 1 1 0 1],[ 2 2 2 1 2 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,0,1,1,2,0,1,1,2,0,1,1,1,2,-1] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,1,2,2,2,1,1,1,1,0,0,0,1,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,2,0,1,1,2,0,0,1,2,0,0,1,1,2,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,1,2,2,2,0,1,1,1,0,0,0,0,1,2] |
| Phi of -K* | [-2,-1,0,0,1,2,-1,1,2,2,2,1,1,1,1,0,0,0,1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+21t^4+17t^2+1 |
| Outer characteristic polynomial | t^7+31t^5+39t^3+5t |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -128*K1**6 + 384*K1**4*K2 - 3200*K1**4 + 32*K1**3*K2*K3 + 32*K1**3*K3*K4 - 128*K1**3*K3 - 1584*K1**2*K2**2 - 224*K1**2*K2*K4 + 5264*K1**2*K2 - 1152*K1**2*K3**2 - 96*K1**2*K3*K5 - 144*K1**2*K4**2 - 3292*K1**2 - 320*K1*K2**2*K3 - 192*K1*K2*K3*K4 + 4304*K1*K2*K3 + 2224*K1*K3*K4 + 328*K1*K4*K5 - 48*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 472*K2**2*K4 - 3044*K2**2 + 208*K2*K3*K5 + 32*K2*K4*K6 - 2080*K3**2 - 916*K4**2 - 140*K5**2 - 4*K6**2 + 3554 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}]] |
| If K is slice | False |