| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.22.139 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 8 x + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.140 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.141 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 12 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 12 x^{2} + 8 x + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.142 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 12 x^{4} + 4 x^{2} + 8 x + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.143 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.144 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.145 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.146 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
