| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.8.1 |
$8$ |
$x^{8} + 8 x^{7} + 32 x^{6} + 82 x^{5} + 148 x^{4} + 184 x^{3} + 137 x^{2} + 44 x + 5$ |
$2$ |
$2$ |
$4$ |
$8$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.8.12.1 |
$8$ |
$x^{8} - 12 x^{7} + 52 x^{6} + 840 x^{5} + 3808 x^{4} + 10224 x^{3} + 17968 x^{2} + 20576 x + 15216$ |
$2$ |
$2$ |
$4$ |
$12$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$1$ |
$[3]$ |
$[3]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2}\right) x + 12 t^{3} + 12 t^{2} + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.8.12.2 |
$8$ |
$x^{8} + 16 x^{7} + 120 x^{6} + 546 x^{5} + 1646 x^{4} + 3352 x^{3} + 4457 x^{2} + 3470 x + 1203$ |
$2$ |
$2$ |
$4$ |
$12$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$1$ |
$[3]$ |
$[3]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + 4 x + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.8.16.1 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 40 x^{5} + 60 x^{4} + 32 x^{3} + 88 x^{2} + 108$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 6\right) x^{2} + 4 x + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.2 |
$8$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 x^{4} + 16 x^{3} + 40 x^{2} + 48 x + 84$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.3 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 8 x^{5} + 36 x^{4} - 32 x^{3} + 88 x^{2} - 32 x + 124$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 x + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.8.22.2 |
$8$ |
$x^{8} + 16 x^{7} + 88 x^{6} + 192 x^{5} + 180 x^{4} + 288 x^{3} + 432 x^{2} + 516$ |
$2$ |
$4$ |
$2$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 12 x^{2} + 16 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.5 |
$8$ |
$x^{8} + 20 x^{7} + 154 x^{6} + 592 x^{5} + 1315 x^{4} + 1968 x^{3} + 2050 x^{2} + 828 x + 111$ |
$2$ |
$4$ |
$2$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 12 x^{2} + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.6 |
$8$ |
$x^{8} + 16 x^{7} + 76 x^{6} + 88 x^{5} + 8 x^{4} + 192 x^{3} + 280 x^{2} + 48 x + 252$ |
$2$ |
$4$ |
$2$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t + 8\right) x^{2} + 8 t x + 12 t + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.7 |
$8$ |
$x^{8} + 20 x^{7} + 154 x^{6} + 592 x^{5} + 1331 x^{4} + 2128 x^{3} + 2386 x^{2} + 764 x + 103$ |
$2$ |
$4$ |
$2$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 12 x^{2} + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.24.1 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 22$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 22$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.10 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.11 |
$8$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 8 x + 26$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 8 x + 26$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.13 |
$8$ |
$x^{8} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.2 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 6$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.5 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 18$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 18$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.7 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 14$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 14$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.9 |
$8$ |
$x^{8} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 30$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 30$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
