| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.20.22 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{6} + 8 x^{5} + 60 x^{4} + 88 x^{3} + 40 x^{2} - 48 x + 36$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 4 t x^{2} + 8 t x + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.24 |
$8$ |
$x^{8} - 4 x^{7} + 20 x^{6} + 32 x^{5} - 4 x^{4} + 8 x^{3} + 88 x^{2} + 96 x + 36$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 4\right) x^{2} + 8 x + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.25 |
$8$ |
$x^{8} - 4 x^{7} + 12 x^{6} + 24 x^{5} + 100 x^{4} + 24 x^{3} + 24 x^{2} - 80 x + 100$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 4 t x^{2} + 8 t x + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.30 |
$8$ |
$x^{8} + 4 x^{7} + 20 x^{6} + 80 x^{5} + 124 x^{4} + 24 x^{3} + 24 x^{2} + 36$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 8\right) x^{2} + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.38 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 48 x^{5} + 148 x^{4} + 8 x^{3} - 24 x^{2} + 4$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 12 t x^{2} + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.40 |
$8$ |
$x^{8} + 4 x^{7} + 28 x^{6} + 40 x^{5} + 84 x^{4} + 8 x^{3} + 88 x^{2} - 16 x + 4$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 8\right) x^{2} + 8 t x + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.41 |
$8$ |
$x^{8} - 4 x^{7} + 4 x^{6} + 96 x^{5} + 172 x^{4} - 56 x^{3} - 168 x^{2} + 196$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 12 t x^{2} + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.46 |
$8$ |
$x^{8} - 4 x^{7} + 16 x^{6} + 24 x^{3} + 12$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 4 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.62 |
$8$ |
$x^{8} - 8 x^{7} + 64 x^{6} + 104 x^{5} + 148 x^{4} + 144 x^{3} + 256 x^{2} + 336 x + 516$ |
$2$ |
$4$ |
$2$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(8 t + 4\right) x^{2} + \left(8 t + 8\right) x + 16 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.63 |
$8$ |
$x^{8} + 8 x^{5} + 44 x^{4} + 64 x^{2} + 176 x + 484$ |
$2$ |
$4$ |
$2$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x + 22$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.64 |
$8$ |
$x^{8} - 8 x^{7} + 76 x^{6} + 96 x^{5} + 152 x^{4} + 16 x^{3} + 120 x^{2} + 28$ |
$2$ |
$4$ |
$2$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(12 t + 12\right) x^{2} + 4 t + 6$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.65 |
$8$ |
$x^{8} - 8 x^{7} + 76 x^{6} + 96 x^{5} + 168 x^{4} + 144 x^{3} + 504 x^{2} + 444$ |
$2$ |
$4$ |
$2$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(12 t + 12\right) x^{2} + 20 t + 22$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.75 |
$8$ |
$x^{8} + 24 x^{6} + 8 x^{5} + 172 x^{4} + 96 x^{3} + 400 x^{2} + 112 x + 196$ |
$2$ |
$4$ |
$2$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 12 x^{2} + \left(8 t + 8\right) x + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.77 |
$8$ |
$x^{8} + 8 x^{7} + 60 x^{6} + 32 x^{5} + 64 x^{4} + 336 x^{3} - 24 x^{2} + 684$ |
$2$ |
$4$ |
$2$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 12 t + 30$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.81 |
$8$ |
$x^{8} + 16 x^{6} + 8 x^{5} + 140 x^{4} + 160 x^{3} + 480 x^{2} + 304 x + 388$ |
$2$ |
$4$ |
$2$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 12\right) x^{2} + \left(8 t + 8\right) x + 16 t + 22$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.82 |
$8$ |
$x^{8} + 8 x^{7} + 68 x^{6} + 160 x^{5} + 144 x^{4} + 272 x^{3} + 280 x^{2} + 364$ |
$2$ |
$4$ |
$2$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(12 t + 8\right) x^{2} + 12 t + 22$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.25.100 |
$8$ |
$x^{8} + 8 x^{5} + 14 x^{4} + 8 x^{3} + 28 x^{2} + 22$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{5} + 14 x^{4} + 8 x^{3} + 28 x^{2} + 22$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.101 |
$8$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 6$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.102 |
$8$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 10 x^{4} + 12 x^{2} + 22$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 10 x^{4} + 12 x^{2} + 22$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.103 |
$8$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 6$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.104 |
$8$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 16 x + 6$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 16 x + 6$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.65 |
$8$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 14$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.66 |
$8$ |
$x^{8} + 14 x^{4} + 8 x^{3} + 4 x^{2} + 30$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 14 x^{4} + 8 x^{3} + 4 x^{2} + 30$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.67 |
$8$ |
$x^{8} + 8 x^{5} + 14 x^{4} + 8 x^{3} + 28 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{5} + 14 x^{4} + 8 x^{3} + 28 x^{2} + 14$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.68 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 10 x^{4} + 12 x^{2} + 30$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 10 x^{4} + 12 x^{2} + 30$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.69 |
$8$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 16 x + 14$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 16 x + 14$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.70 |
$8$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 28 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 28 x^{2} + 14$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.71 |
$8$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 16 x + 14$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 16 x + 14$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.72 |
$8$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 14$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.97 |
$8$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 28 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 28 x^{2} + 6$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.98 |
$8$ |
$x^{8} + 8 x^{6} + 14 x^{4} + 12 x^{2} + 16 x + 6$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 14 x^{4} + 12 x^{2} + 16 x + 6$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.25.99 |
$8$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 22$ |
$2$ |
$8$ |
$1$ |
$25$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 22$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
