| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.8.10 |
$8$ |
$x^{8} - 6 x^{7} + 36 x^{6} - 60 x^{5} + 88 x^{4} + 136 x^{3} + 336 x^{2} + 400 x + 144$ |
$2$ |
$2$ |
$4$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.8.8.7 |
$8$ |
$x^{8} + 8 x^{7} + 40 x^{6} + 120 x^{5} + 232 x^{4} + 240 x^{3} + 160 x^{2} + 64 x + 16$ |
$2$ |
$2$ |
$4$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.8.8.8 |
$8$ |
$x^{8} - 6 x^{7} + 40 x^{6} - 52 x^{5} + 192 x^{4} + 328 x^{3} + 1376 x^{2} + 1264 x + 1328$ |
$2$ |
$2$ |
$4$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t\right) x + 4 t^{3} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.8.8.9 |
$8$ |
$x^{8} + 8 x^{7} + 56 x^{6} + 216 x^{5} + 680 x^{4} + 1296 x^{3} + 2016 x^{2} + 1728 x + 1296$ |
$2$ |
$2$ |
$4$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(2 t^{2} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.8.12.10 |
$8$ |
$x^{8} + 68 x^{6} + 272 x^{5} + 928 x^{4} + 5376 x^{3} + 13680 x^{2} + 15552 x + 92016$ |
$2$ |
$2$ |
$4$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{3} + 12 t^{2} + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.8.12.11 |
$8$ |
$x^{8} + 16 x^{7} + 92 x^{6} + 352 x^{5} + 1264 x^{4} + 2304 x^{3} + 6544 x^{2} - 256 x + 12080$ |
$2$ |
$2$ |
$4$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t + 4\right) x + 4 t^{3} + 12 t^{2} + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.8.12.12 |
$8$ |
$x^{8} + 92 x^{6} + 144 x^{5} + 1232 x^{4} + 5248 x^{3} + 11152 x^{2} + 34752 x + 49072$ |
$2$ |
$2$ |
$4$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t^{2} + 4 t\right) x + 4 t^{3} + 12 t^{2} + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.8.12.9 |
$8$ |
$x^{8} + 16 x^{7} + 68 x^{6} + 192 x^{5} + 1504 x^{4} + 2560 x^{3} + 12016 x^{2} + 13184 x + 15216$ |
$2$ |
$2$ |
$4$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t + 4\right) x + 12 t^{3} + 12 t^{2} + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.8.18.29 |
$8$ |
$x^{8} + 20 x^{6} - 8 x^{5} + 164 x^{4} + 16 x^{3} + 272 x^{2} - 16 x + 76$ |
$2$ |
$4$ |
$2$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 14\right) x^{2} + 8 t x + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.30 |
$8$ |
$x^{8} + 4 x^{7} + 32 x^{6} + 104 x^{5} + 164 x^{4} + 56 x^{3} + 152 x^{2} + 124$ |
$2$ |
$4$ |
$2$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 14\right) x^{2} + 12 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.31 |
$8$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 36 x^{4} + 48 x^{3} + 64 x^{2} + 48 x + 12$ |
$2$ |
$4$ |
$2$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 6 x^{2} + \left(8 t + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.32 |
$8$ |
$x^{8} + 20 x^{6} + 8 x^{5} + 164 x^{4} + 176 x^{3} + 272 x^{2} + 112 x + 76$ |
$2$ |
$4$ |
$2$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 14\right) x^{2} + \left(8 t + 8\right) x + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.41 |
$8$ |
$x^{8} + 8 x^{7} + 44 x^{6} + 112 x^{5} + 188 x^{4} - 32 x^{3} - 112 x^{2} + 124$ |
$2$ |
$4$ |
$2$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 14 x^{2} + 12 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.42 |
$8$ |
$x^{8} + 20 x^{6} + 164 x^{4} + 208 x^{2} + 76$ |
$2$ |
$4$ |
$2$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 14\right) x^{2} + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.43 |
$8$ |
$x^{8} + 28 x^{6} + 212 x^{4} + 224 x^{2} + 76$ |
$2$ |
$4$ |
$2$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 14 x^{2} + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.44 |
$8$ |
$x^{8} + 28 x^{6} + 16 x^{5} + 212 x^{4} + 224 x^{3} + 288 x^{2} + 128 x + 76$ |
$2$ |
$4$ |
$2$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 14 x^{2} + 8 x + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.20.23 |
$8$ |
$x^{8} + 4 x^{7} + 20 x^{6} + 80 x^{5} + 116 x^{4} + 56 x^{3} + 152 x^{2} + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 8\right) x^{2} + 8 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.28 |
$8$ |
$x^{8} - 4 x^{7} + 12 x^{6} + 96 x^{5} + 84 x^{4} + 8 x^{3} + 200 x^{2} + 32 x + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(12 t + 4\right) x^{2} + 8 x + 8 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.29 |
$8$ |
$x^{8} - 4 x^{7} + 20 x^{6} + 16 x^{5} + 20 x^{4} + 40 x^{3} + 56 x^{2} + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.32 |
$8$ |
$x^{8} + 4 x^{7} + 20 x^{6} + 24 x^{5} + 60 x^{4} + 104 x^{3} + 136 x^{2} + 48 x + 84$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 8 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.43 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{6} + 64 x^{5} + 132 x^{4} + 88 x^{3} + 104 x^{2} + 148$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 4\right) x^{2} + 8 t + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.44 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{6} + 56 x^{5} + 164 x^{4} + 248 x^{3} + 168 x^{2} + 16 x + 148$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 4\right) x^{2} + 8 t x + 8 t + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.45 |
$8$ |
$x^{8} + 4 x^{7} + 16 x^{6} + 8 x^{4} + 40 x^{3} + 28$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 4 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.48 |
$8$ |
$x^{8} - 4 x^{7} + 16 x^{6} + 8 x^{4} + 56 x^{3} + 124$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.59 |
$8$ |
$x^{8} + 8 x^{7} + 64 x^{6} + 104 x^{5} + 164 x^{4} + 336 x^{3} + 352 x^{2} + 240 x + 468$ |
$2$ |
$4$ |
$2$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t + 4\right) x^{2} + \left(8 t + 8\right) x + 24 t + 6$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.60 |
$8$ |
$x^{8} + 16 x^{7} + 76 x^{6} + 96 x^{5} + 120 x^{4} - 192 x^{3} + 360 x^{2} + 732$ |
$2$ |
$4$ |
$2$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(12 t + 12\right) x^{2} + 28 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.61 |
$8$ |
$x^{8} + 16 x^{6} + 8 x^{5} + 60 x^{4} + 64 x^{3} + 32 x^{2} + 80 x + 52$ |
$2$ |
$4$ |
$2$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{2} + \left(8 t + 8\right) x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.66 |
$8$ |
$x^{8} + 16 x^{6} + 8 x^{5} + 116 x^{4} + 160 x^{3} + 192 x^{2} + 112 x + 52$ |
$2$ |
$4$ |
$2$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 12\right) x^{2} + \left(8 t + 8\right) x + 8 t + 6$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.76 |
$8$ |
$x^{8} + 16 x^{6} + 8 x^{5} + 140 x^{4} + 160 x^{3} + 576 x^{2} + 400 x + 628$ |
$2$ |
$4$ |
$2$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 12\right) x^{2} + \left(8 t + 8\right) x + 24 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.78 |
$8$ |
$x^{8} - 8 x^{7} + 84 x^{6} - 32 x^{5} + 144 x^{4} + 208 x^{3} + 488 x^{2} + 844$ |
$2$ |
$4$ |
$2$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t + 12\right) x^{2} + 28 t + 30$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.79 |
$8$ |
$x^{8} + 8 x^{7} + 80 x^{6} + 72 x^{5} + 212 x^{4} + 240 x^{3} + 224 x^{2} + 176 x + 148$ |
$2$ |
$4$ |
$2$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 8 x^{2} + \left(8 t + 8\right) x + 8 t + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.80 |
$8$ |
$x^{8} + 8 x^{7} + 64 x^{6} + 8 x^{5} + 148 x^{4} + 368 x^{3} + 64 x^{2} + 368 x + 532$ |
$2$ |
$4$ |
$2$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t + 8\right) x + 24 t + 22$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.30.1 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 20 x^{4} + 18$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 20 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.10 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 10$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 10$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.11 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 20 x^{4} + 26$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 20 x^{4} + 26$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.12 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 4 x^{4} + 26$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 4 x^{4} + 26$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.14 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{5} + 20 x^{4} + 26$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{5} + 20 x^{4} + 26$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.15 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 2$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.16 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 4 x^{4} + 10$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 4 x^{4} + 10$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.18 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 20 x^{4} + 2$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 20 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.20 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 20 x^{4} + 26$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 20 x^{4} + 26$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.25 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 16 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 16 x^{2} + 10$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.26 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 26$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 26$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.27 |
$8$ |
$x^{8} + 8 x^{7} + 20 x^{4} + 10$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 20 x^{4} + 10$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.28 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 20 x^{4} + 18$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 20 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.29 |
$8$ |
$x^{8} + 8 x^{7} + 20 x^{4} + 18$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 20 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.3 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 20 x^{4} + 10$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 20 x^{4} + 10$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.33 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 20 x^{4} + 10$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 20 x^{4} + 10$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.34 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{5} + 4 x^{4} + 2$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{5} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
| 2.8.30.37 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 20 x^{4} + 10$ |
$2$ |
$8$ |
$1$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, 19/4]$ |
$[2, 3, 7/2, 4, 17/4, 19/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 20 x^{4} + 10$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
