| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.18.1 |
$8$ |
$x^{8} + 8 x^{7} + 40 x^{6} + 112 x^{5} + 232 x^{4} + 240 x^{3} + 256 x^{2} + 96 x + 84$ |
$2$ |
$4$ |
$2$ |
$18$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 14\right) x^{2} + 8 x + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.10 |
$8$ |
$x^{8} - 4 x^{7} + 26 x^{6} + 8 x^{5} + 132 x^{4} + 72 x^{3} + 252 x^{2} + 80 x + 172$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t + 8\right) x^{2} + 8 t x + 12 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.11 |
$8$ |
$x^{8} + 8 x^{7} + 10 x^{6} - 16 x^{5} + 80 x^{4} + 96 x^{3} + 100 x^{2} + 144 x + 84$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 6 t x^{2} + \left(8 t + 8\right) x + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.12 |
$8$ |
$x^{8} + 8 x^{7} + 30 x^{6} + 48 x^{5} + 168 x^{4} + 128 x^{3} + 92 x^{2} - 16 x + 4$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(14 t + 14\right) x^{2} + 8 t x + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.13 |
$8$ |
$x^{8} + 8 x^{7} + 14 x^{6} - 16 x^{5} + 8 x^{4} + 128 x^{3} + 124 x^{2} + 48 x + 84$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t + 2\right) x^{2} + 8 t x + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.14 |
$8$ |
$x^{8} + 8 x^{7} + 30 x^{6} + 48 x^{5} + 72 x^{4} + 128 x^{3} + 260 x^{2} - 112 x + 196$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t + 10\right) x^{2} + 8 t x + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.15 |
$8$ |
$x^{8} - 2 x^{6} - 8 x^{5} + 96 x^{4} + 128 x^{3} + 164 x^{2} + 16 x + 148$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(10 t + 4\right) x^{2} + 8 t x + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.16 |
$8$ |
$x^{8} - 14 x^{6} - 8 x^{5} + 216 x^{4} + 224 x^{3} + 92 x^{2} + 16 x + 148$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 14 t x^{2} + 8 t x + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.17 |
$8$ |
$x^{8} + 8 x^{7} + 28 x^{6} + 48 x^{5} + 56 x^{4} + 80 x^{3} + 120 x^{2} + 148$ |
$2$ |
$4$ |
$2$ |
$18$ |
$C_2^3: C_4$ (as 8T21) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 6 x^{2} + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.18 |
$8$ |
$x^{8} + 28 x^{6} + 8 x^{5} + 224 x^{4} + 112 x^{3} + 456 x^{2} + 112 x + 196$ |
$2$ |
$4$ |
$2$ |
$18$ |
$C_2^3: C_4$ (as 8T21) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 14 x^{2} + \left(8 t + 8\right) x + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.19 |
$8$ |
$x^{8} + 4 x^{7} + 36 x^{6} + 88 x^{5} + 168 x^{4} + 88 x^{3} + 296 x^{2} + 148$ |
$2$ |
$4$ |
$2$ |
$18$ |
$C_2^3: C_4$ (as 8T21) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(8 t + 14\right) x^{2} + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.2 |
$8$ |
$x^{8} + 4 x^{7} + 38 x^{6} + 116 x^{5} + 409 x^{4} + 816 x^{3} + 1332 x^{2} + 1260 x + 441$ |
$2$ |
$4$ |
$2$ |
$18$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 14 x^{2} + 8 x + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.20 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 40 x^{4} + 64 x^{3} + 160 x^{2} + 96 x + 84$ |
$2$ |
$4$ |
$2$ |
$18$ |
$C_2^3: C_4$ (as 8T21) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 6\right) x^{2} + 8 x + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.21 |
$8$ |
$x^{8} - 4 x^{7} + 10 x^{6} + 48 x^{5} + 36 x^{4} + 72 x^{3} + 108 x^{2} + 108$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 6 t x^{2} + 12 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.22 |
$8$ |
$x^{8} + 8 x^{7} + 6 x^{6} - 24 x^{5} + 248 x^{4} - 32 x^{3} + 172 x^{2} + 96 x + 84$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(14 t + 2\right) x^{2} + 8 x + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.23 |
$8$ |
$x^{8} + 14 x^{6} + 16 x^{5} + 136 x^{4} + 112 x^{3} + 148 x^{2} + 96 x + 36$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(10 t + 12\right) x^{2} + 8 x + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.24 |
$8$ |
$x^{8} - 4 x^{7} + 34 x^{6} - 24 x^{5} + 100 x^{4} + 40 x^{3} + 180 x^{2} + 172$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t + 10\right) x^{2} + 12 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.25 |
$8$ |
$x^{8} + 8 x^{7} + 30 x^{6} + 64 x^{5} + 232 x^{4} + 240 x^{3} + 260 x^{2} + 112 x + 52$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(14 t + 14\right) x^{2} + \left(8 t + 8\right) x + 8 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.26 |
$8$ |
$x^{8} - 2 x^{6} + 16 x^{5} + 32 x^{4} - 16 x^{3} + 36 x^{2} + 224 x + 196$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 t x^{2} + 8 x + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.27 |
$8$ |
$x^{8} + 8 x^{7} + 22 x^{6} + 32 x^{5} + 72 x^{4} + 112 x^{3} + 76 x^{2} + 16 x + 4$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t + 6\right) x^{2} + \left(8 t + 8\right) x + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.28 |
$8$ |
$x^{8} + 8 x^{7} + 18 x^{6} + 8 x^{5} + 152 x^{4} + 16 x^{3} + 4 x^{2} + 4$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(14 t + 8\right) x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 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) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 14\right) x^{2} + 8 t x + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.3 |
$8$ |
$x^{8} + 8 x^{7} + 40 x^{6} + 88 x^{5} + 136 x^{4} + 208 x^{2} - 48 x + 36$ |
$2$ |
$4$ |
$2$ |
$18$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 14\right) x^{2} + 8 t x + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 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) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 14\right) x^{2} + \left(8 t + 8\right) x + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.33 |
$8$ |
$x^{8} + 4 x^{7} + 18 x^{6} + 16 x^{5} + 40 x^{3} + 20 x^{2} + 52$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t + 2\right) x^{2} + 8 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.34 |
$8$ |
$x^{8} + 4 x^{7} + 10 x^{6} + 48 x^{5} + 80 x^{4} + 40 x^{3} + 132 x^{2} + 52$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(10 t + 2\right) x^{2} + 8 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.35 |
$8$ |
$x^{8} + 6 x^{6} + 8 x^{5} + 36 x^{4} + 96 x^{3} + 100 x^{2} + 48 x + 12$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(6 t + 6\right) x^{2} + \left(8 t + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.36 |
$8$ |
$x^{8} - 2 x^{6} + 8 x^{5} + 148 x^{4} + 160 x^{3} + 148 x^{2} + 48 x + 12$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(14 t + 6\right) x^{2} + \left(8 t + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.37 |
$8$ |
$x^{8} + 8 x^{7} + 10 x^{6} - 16 x^{5} + 68 x^{4} + 48 x^{3} + 100 x^{2} + 48 x + 12$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 6 t x^{2} + \left(8 t + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.38 |
$8$ |
$x^{8} - 10 x^{6} - 8 x^{5} + 180 x^{4} + 208 x^{3} + 108 x^{2} + 16 x + 28$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(14 t + 2\right) x^{2} + 8 t x + 4 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.39 |
$8$ |
$x^{8} + 8 x^{7} + 18 x^{6} + 108 x^{4} + 128 x^{3} + 308 x^{2} + 176 x + 124$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(14 t + 8\right) x^{2} + 8 t x + 12 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.4 |
$8$ |
$x^{8} - 4 x^{7} + 40 x^{6} - 24 x^{5} + 168 x^{4} - 24 x^{3} + 144 x^{2} + 36$ |
$2$ |
$4$ |
$2$ |
$18$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 14\right) x^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.40 |
$8$ |
$x^{8} + 6 x^{6} - 8 x^{5} + 60 x^{4} + 48 x^{3} + 172 x^{2} - 48 x + 156$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(6 t + 6\right) x^{2} + 8 t x + 4 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 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) |
$4$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 14 x^{2} + 8 x + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.45 |
$8$ |
$x^{8} + 8 x^{7} + 18 x^{6} + 4 x^{4} + 96 x^{3} + 180 x^{2} + 112 x + 124$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t + 4\right) x^{2} + 8 t x + 12 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.46 |
$8$ |
$x^{8} + 14 x^{6} + 8 x^{5} + 84 x^{4} + 128 x^{3} + 156 x^{2} + 80 x + 28$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(6 t + 10\right) x^{2} + \left(8 t + 8\right) x + 4 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.47 |
$8$ |
$x^{8} + 8 x^{7} + 30 x^{6} + 72 x^{5} + 284 x^{4} + 208 x^{3} + 316 x^{2} + 192 x + 156$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(14 t + 14\right) x^{2} + 8 x + 4 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.48 |
$8$ |
$x^{8} + 14 x^{6} + 16 x^{5} + 84 x^{4} + 112 x^{3} + 156 x^{2} + 64 x + 28$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(6 t + 10\right) x^{2} + 8 x + 4 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.49 |
$8$ |
$x^{8} - 10 x^{6} + 8 x^{5} + 116 x^{4} + 80 x^{3} + 164 x^{2} + 208 x + 172$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 10 t x^{2} + \left(8 t + 8\right) x + 12 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.5 |
$8$ |
$x^{8} + 4 x^{7} + 16 x^{6} + 72 x^{5} + 128 x^{4} + 40 x^{3} + 100$ |
$2$ |
$4$ |
$2$ |
$18$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 6\right) x^{2} + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.50 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 40 x^{5} + 104 x^{4} + 8 x^{3} - 20 x^{2} + 4$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 10 t x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.51 |
$8$ |
$x^{8} + 22 x^{6} - 8 x^{5} + 148 x^{4} - 16 x^{3} + 100 x^{2} + 48 x + 12$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(6 t + 14\right) x^{2} + 8 t x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.52 |
$8$ |
$x^{8} + 14 x^{6} + 196 x^{4} + 84 x^{2} + 12$ |
$2$ |
$4$ |
$2$ |
$18$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(14 t + 14\right) x^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.53 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$18$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 2, 3]$ |
$[2, 2, 3]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{3} + 2$ |
$[11, 6, 6, 0]$ |
$[1, 2]$ |
| 2.8.18.54 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$ |
$2$ |
$8$ |
$1$ |
$18$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 2, 3]$ |
$[2, 2, 3]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$ |
$[11, 6, 6, 0]$ |
$[1, 2]$ |
