| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.10.2 |
$8$ |
$x^{8} + 2 x^{3} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$10$ |
$\textrm{GL(2,3)}$ (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) |
$2$ |
$3$ |
$[4/3, 4/3, 3/2]$ |
$[4/3, 4/3, 3/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.12.29 |
$8$ |
$x^{8} + 2 x^{5} + 2 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$12$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[4/3, 4/3, 2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{5} + 2 x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.12.30 |
$8$ |
$x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$12$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[4/3, 4/3, 2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.71 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 6 x^{2} + 4 x + 10$ |
$2$ |
$8$ |
$1$ |
$16$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[4/3, 4/3, 3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 6 x^{2} + 4 x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.72 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2 x^{2} + 4 x + 10$ |
$2$ |
$8$ |
$1$ |
$16$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[4/3, 4/3, 3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2 x^{2} + 4 x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.73 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 2 x^{2} + 4 x + 2$ |
$2$ |
$8$ |
$1$ |
$16$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[4/3, 4/3, 3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.74 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 6 x^{2} + 4 x + 2$ |
$2$ |
$8$ |
$1$ |
$16$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[4/3, 4/3, 3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 6 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.22.131 |
$8$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 4 x^{2} + 8 x + 10$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.132 |
$8$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 10$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.133 |
$8$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 12 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.134 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.135 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 12 x^{2} + 8 x + 10$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.136 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{2} + 8 x + 10$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.137 |
$8$ |
$x^{8} + 4 x^{7} + 8 x^{3} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 8 x^{3} + 4 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.138 |
$8$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
