| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.14.1 |
$8$ |
$x^{8} + 2 x^{7} + 6$ |
$2$ |
$8$ |
$1$ |
$14$ |
$A_4\times C_2$ (as 8T13) |
$3$ |
$1$ |
$[2, 2, 2]$ |
$[2, 2, 2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 6$ |
$[7, 7, 7, 0]$ |
$[3]$ |
| 2.8.14.10 |
$8$ |
$x^{8} + 2 x^{7} + 2 x^{2} + 4 x + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 5/2]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{2} + 4 x + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.14.11 |
$8$ |
$x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 5/2]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.14.12 |
$8$ |
$x^{8} + 2 x^{7} + 4 x^{4} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 5/2]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 4 x^{4} + 2 x^{2} + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.14.13 |
$8$ |
$x^{8} + 2 x^{7} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 5/2]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{2} + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.14.14 |
$8$ |
$x^{8} + 2 x^{7} + 4 x^{3} + 2 x^{2} + 4 x + 6$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 5/2]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 4 x^{3} + 2 x^{2} + 4 x + 6$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.14.2 |
$8$ |
$x^{8} + 2 x^{7} + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$A_4\times C_2$ (as 8T13) |
$3$ |
$1$ |
$[2, 2, 2]$ |
$[2, 2, 2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2$ |
$[7, 7, 7, 0]$ |
$[3]$ |
| 2.8.14.3 |
$8$ |
$x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2^3 : C_4 $ (as 8T19) |
$4$ |
$1$ |
$[2, 2, 2]$ |
$[2, 2, 2]^{4}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 2$ |
$[7, 6, 4, 0]$ |
$[4]$ |
| 2.8.14.4 |
$8$ |
$x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 6$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2^3 : C_4 $ (as 8T19) |
$4$ |
$1$ |
$[2, 2, 2]$ |
$[2, 2, 2]^{4}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 6$ |
$[7, 6, 4, 0]$ |
$[4]$ |
| 2.8.14.5 |
$8$ |
$x^{8} + 2 x^{7} + 2 x^{6} + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2^3:C_7$ (as 8T25) |
$7$ |
$1$ |
$[2, 2, 2]$ |
$[2, 2, 2]^{7}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{6} + 2$ |
$[7, 6, 6, 0]$ |
$[7]$ |
| 2.8.14.6 |
$8$ |
$x^{8} + 2 x^{7} + 2 x^{4} + 6$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2^3:C_7$ (as 8T25) |
$7$ |
$1$ |
$[2, 2, 2]$ |
$[2, 2, 2]^{7}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{4} + 6$ |
$[7, 7, 4, 0]$ |
$[7]$ |
| 2.8.14.7 |
$8$ |
$x^{8} + 2 x^{7} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 5/2]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 4 x^{3} + 2 x^{2} + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.14.8 |
$8$ |
$x^{8} + 2 x^{7} + 4 x^{3} + 6 x^{2} + 4 x + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 5/2]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 4 x^{3} + 6 x^{2} + 4 x + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.14.9 |
$8$ |
$x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2 \wr S_4$ (as 8T44) |
$2$ |
$3$ |
$[4/3, 4/3, 5/2]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
