Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.8.10.1 |
$8$ |
$x^{8} + 2 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$10$ |
$C_2^3:(C_7: C_3)$ (as 8T36) |
$3$ |
$7$ |
$[10/7, 10/7, 10/7]$ |
$[10/7, 10/7, 10/7]_{7}^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{3} + 2$ |
$[3, 3, 3, 0]$ |
$[1]$ |
2.8.10.2 |
$8$ |
$x^{8} + 2 x^{3} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$10$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[4/3, 4/3, 3/2]$ |
$[4/3, 4/3, 3/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{3} + 2 x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
2.8.10.3 |
$8$ |
$x^{8} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$10$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[4/3, 4/3, 3/2]$ |
$[4/3, 4/3, 3/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |