| $x^{8} + 2 a_{6} x^{6} + \left(2 b_{4} + 4 c_{12}\right) x^{4} + 4 b_{11} x^{3} + 4 a_{9} x + 4 c_{8} + 2$ |
| Indices of inseparability: | $[9,6,4,0]$ (show 4), $[9,6,6,0]$ (show 6) |
| Associated inertia: | $[2,1]$ (show 6), $[3,1]$ (show 4) |
| Jump Set: | $[1,2,7,15]$ (show 4), $[1,3,6,16]$ (show 3), $[1,3,9,17]$ (show 3) |
Select desired size of Galois group.
| | Galois groups of order 16 |
|---|
|
|
$\SD_{16}$
(as 8T8) |
|
hidden slopes
|
$[\ ]^{2}$ |
2 |
|
| Label |
Packet size |
Polynomial |
Galois group |
Galois degree |
$\#\Aut(K/\Q_p)$ |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 2.1.8.16c2.1 |
4 |
$x^{8} + 2 x^{6} + 2 x^{4} + 4 x + 2$ |
$C_2\wr A_4$ (as 8T38) |
$192$ |
$2$ |
$[2, 2, 2, 2, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2}]^{6}$ |
$[2,2]^{6}$ |
$[1,1]^{6}$ |
$[9, 6, 4, 0]$ |
$[3, 1]$ |
$z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 15]$ |
| 2.1.8.16c2.2 |
4 |
$x^{8} + 2 x^{6} + 6 x^{4} + 4 x + 2$ |
$C_2\wr A_4$ (as 8T38) |
$192$ |
$2$ |
$[2, 2, 2, 2, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2}]^{6}$ |
$[2,2]^{6}$ |
$[1,1]^{6}$ |
$[9, 6, 4, 0]$ |
$[3, 1]$ |
$z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 15]$ |
| 2.1.8.16c2.3 |
4 |
$x^{8} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x + 2$ |
$C_2\wr A_4$ (as 8T38) |
$192$ |
$2$ |
$[2, 2, 2, 2, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2}]^{6}$ |
$[2,2]^{6}$ |
$[1,1]^{6}$ |
$[9, 6, 4, 0]$ |
$[3, 1]$ |
$z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 15]$ |
| 2.1.8.16c2.4 |
4 |
$x^{8} + 2 x^{6} + 6 x^{4} + 4 x^{3} + 4 x + 2$ |
$C_2\wr A_4$ (as 8T38) |
$192$ |
$2$ |
$[2, 2, 2, 2, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2}]^{6}$ |
$[2,2]^{6}$ |
$[1,1]^{6}$ |
$[9, 6, 4, 0]$ |
$[3, 1]$ |
$z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 15]$ |
Download
displayed columns for
results
