| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,1,0,1,1,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1719', '7.40949'] |
| Arrow polynomial of the knot is: -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.239', '6.428', '6.470', '6.556', '6.700', '6.910', '6.962', '6.1006', '6.1013', '6.1038', '6.1207', '6.1224', '6.1225', '6.1269', '6.1270', '6.1308', '6.1319', '6.1320', '6.1323', '6.1485', '6.1551', '6.1579', '6.1581', '6.1660', '6.1672', '6.1679', '6.1711', '6.1719', '6.1732', '6.1745', '6.1748', '6.1827', '6.1836', '6.1838', '6.1850', '6.1866'] |
| Outer characteristic polynomial of the knot is: t^7+22t^5+46t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1719', '6.1832', '7.40949'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 1664*K1**4*K2 - 5600*K1**4 + 448*K1**3*K2*K3 + 64*K1**3*K3*K4 - 2080*K1**3*K3 + 96*K1**2*K2**3 - 2832*K1**2*K2**2 - 576*K1**2*K2*K4 + 8680*K1**2*K2 - 1344*K1**2*K3**2 - 128*K1**2*K3*K5 - 288*K1**2*K4**2 - 3832*K1**2 - 64*K1*K2**2*K3 - 32*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 5592*K1*K2*K3 + 1912*K1*K3*K4 + 448*K1*K4*K5 - 88*K2**4 - 16*K2**2*K3**2 - 16*K2**2*K4**2 + 424*K2**2*K4 - 3492*K2**2 + 128*K2*K3*K5 + 32*K2*K4*K6 - 1884*K3**2 - 742*K4**2 - 164*K5**2 - 12*K6**2 + 3892 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1719'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4835', 'vk6.5179', 'vk6.6400', 'vk6.6831', 'vk6.8369', 'vk6.8797', 'vk6.9733', 'vk6.10037', 'vk6.11620', 'vk6.11973', 'vk6.12962', 'vk6.20461', 'vk6.20734', 'vk6.21814', 'vk6.27845', 'vk6.29353', 'vk6.31431', 'vk6.32605', 'vk6.39279', 'vk6.39774', 'vk6.41457', 'vk6.46334', 'vk6.47580', 'vk6.47909', 'vk6.49061', 'vk6.49889', 'vk6.51319', 'vk6.51537', 'vk6.53211', 'vk6.57320', 'vk6.62006', 'vk6.64300'] |
| 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 | O1O2O3U1U4O5O6U5U3O4U6U2 |
| R3 orbit | {'O1O2O3U1U4O5O6U5U3O4U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U4O5U1U6O4O6U5U3 |
| Gauss code of K* | O1O2U3O4O5U6U5U2O6O3U1U4 |
| Gauss code of -K* | O1O2U3O4O5U2U5O3O6U4U1U6 |
| 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 1 0 -1 1],[ 2 0 2 1 1 0 1],[-1 -2 0 0 -1 -1 1],[-1 -1 0 0 -1 0 1],[ 0 -1 1 1 0 -1 0],[ 1 0 1 0 1 0 1],[-1 -1 -1 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 -1 0 -1],[-1 -1 0 -1 0 -1 -1],[-1 0 1 0 -1 -1 -2],[ 0 1 0 1 0 -1 -1],[ 1 0 1 1 1 0 0],[ 2 1 1 2 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,1,0,1,1,0,1,1,1,1,2,1,1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,1,0,1,1,0,-1] |
| Phi of -K | [-2,-1,0,1,1,1,1,1,1,2,2,0,1,1,2,0,1,0,-1,0,1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,-1,1,1,2,0,0,1,1,0,2,2,0,1,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,1,0,1,1,0,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 2z^2+21z+35 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+21w^2z+35w |
| Inner characteristic polynomial | t^6+14t^4+25t^2 |
| Outer characteristic polynomial | t^7+22t^5+46t^3+5t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -128*K1**6 + 1664*K1**4*K2 - 5600*K1**4 + 448*K1**3*K2*K3 + 64*K1**3*K3*K4 - 2080*K1**3*K3 + 96*K1**2*K2**3 - 2832*K1**2*K2**2 - 576*K1**2*K2*K4 + 8680*K1**2*K2 - 1344*K1**2*K3**2 - 128*K1**2*K3*K5 - 288*K1**2*K4**2 - 3832*K1**2 - 64*K1*K2**2*K3 - 32*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 5592*K1*K2*K3 + 1912*K1*K3*K4 + 448*K1*K4*K5 - 88*K2**4 - 16*K2**2*K3**2 - 16*K2**2*K4**2 + 424*K2**2*K4 - 3492*K2**2 + 128*K2*K3*K5 + 32*K2*K4*K6 - 1884*K3**2 - 742*K4**2 - 164*K5**2 - 12*K6**2 + 3892 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}], [{4, 6}, {2, 5}, {1, 3}], [{6}, {2, 5}, {4}, {1, 3}]] |
| If K is slice | False |