| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.12.16 |
$8$ |
$x^{8} + 8 x^{7} + 32 x^{6} + 78 x^{5} + 137 x^{4} + 186 x^{3} + 128 x^{2} - 10 x + 7$ |
$2$ |
$4$ |
$2$ |
$12$ |
$A_4\times C_2$ (as 8T13) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{6}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{3} + 2 x^{2} + 6$ |
$[3, 2, 0]$ |
$[3]$ |
| 2.8.14.1 |
$8$ |
$x^{8} + 2 x^{7} + 6$ |
$2$ |
$8$ |
$1$ |
$14$ |
$A_4\times C_2$ (as 8T13) |
$3$ |
$1$ |
$[2, 2, 2]$ |
$[2, 2, 2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 6$ |
$[7, 7, 7, 0]$ |
$[3]$ |
| 2.8.14.2 |
$8$ |
$x^{8} + 2 x^{7} + 2$ |
$2$ |
$8$ |
$1$ |
$14$ |
$A_4\times C_2$ (as 8T13) |
$3$ |
$1$ |
$[2, 2, 2]$ |
$[2, 2, 2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2$ |
$[7, 7, 7, 0]$ |
$[3]$ |
| 2.8.18.57 |
$8$ |
$x^{8} + 6 x^{6} + 6 x^{4} + 4 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$18$ |
$A_4\times C_2$ (as 8T13) |
$3$ |
$1$ |
$[2, 2, 3]$ |
$[2, 2, 3]^{3}$ |
$t + 1$ |
$x^{8} + 6 x^{6} + 6 x^{4} + 4 x^{3} + 10$ |
$[11, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.18.58 |
$8$ |
$x^{8} + 6 x^{6} + 2 x^{4} + 4 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$18$ |
$A_4\times C_2$ (as 8T13) |
$3$ |
$1$ |
$[2, 2, 3]$ |
$[2, 2, 3]^{3}$ |
$t + 1$ |
$x^{8} + 6 x^{6} + 2 x^{4} + 4 x^{3} + 10$ |
$[11, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.18.59 |
$8$ |
$x^{8} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$18$ |
$A_4\times C_2$ (as 8T13) |
$3$ |
$1$ |
$[2, 2, 3]$ |
$[2, 2, 3]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 2$ |
$[11, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.18.60 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$18$ |
$A_4\times C_2$ (as 8T13) |
$3$ |
$1$ |
$[2, 2, 3]$ |
$[2, 2, 3]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[11, 6, 4, 0]$ |
$[1, 3]$ |
