| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.12.13 |
$8$ |
$x^{8} + 8 x^{7} + 28 x^{6} + 58 x^{5} + 87 x^{4} + 98 x^{3} + 58 x^{2} - 2 x + 1$ |
$2$ |
$4$ |
$2$ |
$12$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{3} + 2$ |
$[3, 3, 0]$ |
$[1]$ |
| 2.8.12.14 |
$8$ |
$x^{8} + 8 x^{7} + 28 x^{6} + 58 x^{5} + 95 x^{4} + 130 x^{3} + 58 x^{2} - 58 x + 13$ |
$2$ |
$4$ |
$2$ |
$12$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{3} + 6$ |
$[3, 3, 0]$ |
$[1]$ |
| 2.8.16.4 |
$8$ |
$x^{8} + 12 x^{7} + 58 x^{6} + 160 x^{5} + 329 x^{4} + 500 x^{3} + 408 x^{2} + 68 x + 61$ |
$2$ |
$4$ |
$2$ |
$16$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.5 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{6} + 36 x^{5} + 73 x^{4} + 88 x^{3} + 48 x^{2} + 56 x + 61$ |
$2$ |
$4$ |
$2$ |
$16$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.8.22.1 |
$8$ |
$x^{8} + 16 x^{7} + 68 x^{6} + 24 x^{5} + 48 x^{4} + 128 x^{3} + 280 x^{2} + 144 x + 108$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(12 t + 8\right) x^{2} + 8 t x + 12 t + 6$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.8 |
$8$ |
$x^{8} + 20 x^{7} + 146 x^{6} + 520 x^{5} + 1239 x^{4} + 2240 x^{3} + 2470 x^{2} + 900 x + 475$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.83 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 4 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 4 x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.84 |
$8$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 4 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 4 x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.85 |
$8$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.86 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 12 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 12 x^{2} + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.87 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.88 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.89 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.90 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 12 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.14 |
$8$ |
$x^{8} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.15 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.3 |
$8$ |
$x^{8} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 18$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 18$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.6 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 26$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 26$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
