| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.22.3 |
$8$ |
$x^{8} + 8 x^{7} + 60 x^{6} + 136 x^{5} + 256 x^{4} + 240 x^{3} + 104 x^{2} + 112 x + 76$ |
$2$ |
$4$ |
$2$ |
$22$ |
$Q_8$ (as 8T5) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(12 t + 4\right) x^{2} + \left(8 t + 8\right) x + 4 t + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.4 |
$8$ |
$x^{8} + 16 x^{7} + 68 x^{6} + 24 x^{5} + 48 x^{4} + 128 x^{3} + 568 x^{2} + 336 x + 588$ |
$2$ |
$4$ |
$2$ |
$22$ |
$Q_8$ (as 8T5) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(12 t + 8\right) x^{2} + 8 t x + 28 t + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.24.12 |
$8$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 14$ |
$2$ |
$8$ |
$1$ |
$24$ |
$Q_8$ (as 8T5) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 14$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.16 |
$8$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 6$ |
$2$ |
$8$ |
$1$ |
$24$ |
$Q_8$ (as 8T5) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.4 |
$8$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 30$ |
$2$ |
$8$ |
$1$ |
$24$ |
$Q_8$ (as 8T5) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 30$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.8 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 6$ |
$2$ |
$8$ |
$1$ |
$24$ |
$Q_8$ (as 8T5) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
