| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.17.1 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 10 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 10 x^{2} + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.10 |
$8$ |
$x^{8} + 2 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{2} + 8 x + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.11 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 2 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 2 x^{2} + 8 x + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.12 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.13 |
$8$ |
$x^{8} + 10 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 10 x^{2} + 8 x + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.14 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 10 x^{2} + 8 x + 6$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 10 x^{2} + 8 x + 6$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.15 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 14$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.16 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 10 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 10 x^{2} + 8 x + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.17 |
$8$ |
$x^{8} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 8 x + 14$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 8 x + 14$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.18 |
$8$ |
$x^{8} + 4 x^{5} + 14 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{5} + 14 x^{2} + 8 x + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.19 |
$8$ |
$x^{8} + 4 x^{4} + 4 x^{3} + 14 x^{2} + 8 x + 14$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{4} + 4 x^{3} + 14 x^{2} + 8 x + 14$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.2 |
$8$ |
$x^{8} + 10 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 10 x^{2} + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.20 |
$8$ |
$x^{8} + 4 x^{5} + 6 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{5} + 6 x^{2} + 8 x + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.21 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.22 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 6 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 6 x^{2} + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.23 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 14 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 14 x^{2} + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.24 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.25 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 14 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 14 x^{2} + 8 x + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.26 |
$8$ |
$x^{8} + 4 x^{5} + 6 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{5} + 6 x^{2} + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.27 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 8 x + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.28 |
$8$ |
$x^{8} + 4 x^{5} + 14 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{5} + 14 x^{2} + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.29 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 6 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 6 x^{2} + 8 x + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.3 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.30 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 14 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 14 x^{2} + 8 x + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.31 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 8 x + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.32 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 14 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 14 x^{2} + 8 x + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.4 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 2 x^{2} + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.5 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 10 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 10 x^{2} + 8 x + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.6 |
$8$ |
$x^{8} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{2} + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.7 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 10 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 10 x^{2} + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.8 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 8 x + 10$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.17.9 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 10 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$17$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 13/4]$ |
$[4/3, 4/3, 3, 19/6, 19/6, 13/4]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 10 x^{2} + 8 x + 2$ |
$[10, 2, 2, 0]$ |
$[1, 1]$ |
