Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.8.16.10 |
$8$ |
$x^{8} + 8 x^{7} + 18 x^{6} + 4 x^{5} - 12 x^{4} + 8 x^{3} + 52 x^{2} + 72 x + 108$ |
$2$ |
$4$ |
$2$ |
$16$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t + 2\right) x^{2} + 4 t x + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.8.16.11 |
$8$ |
$x^{8} + 2 x^{6} - 4 x^{5} + 20 x^{4} + 8 x^{3} + 44 x^{2} - 8 x + 76$ |
$2$ |
$4$ |
$2$ |
$16$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(2 t + 2\right) x^{2} + 4 t x + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.8.16.13 |
$8$ |
$x^{8} + 8 x^{7} + 18 x^{6} + 4 x^{5} - 8 x^{4} + 24 x^{3} + 20 x^{2} - 8 x + 4$ |
$2$ |
$4$ |
$2$ |
$16$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t + 2\right) x^{2} + 4 t x + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.8.16.16 |
$8$ |
$x^{8} + 8 x^{7} + 26 x^{6} + 36 x^{5} + 40 x^{4} + 104 x^{3} + 156 x^{2} - 56 x + 196$ |
$2$ |
$4$ |
$2$ |
$16$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t + 6\right) x^{2} + 4 t x + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
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) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 14\right) x^{2} + 8 x + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
2.8.18.2 |
$8$ |
$x^{8} + 4 x^{7} + 38 x^{6} + 116 x^{5} + 409 x^{4} + 816 x^{3} + 1332 x^{2} + 1260 x + 441$ |
$2$ |
$4$ |
$2$ |
$18$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 14 x^{2} + 8 x + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
2.8.18.4 |
$8$ |
$x^{8} - 4 x^{7} + 40 x^{6} - 24 x^{5} + 168 x^{4} - 24 x^{3} + 144 x^{2} + 36$ |
$2$ |
$4$ |
$2$ |
$18$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 14\right) x^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
2.8.18.53 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$18$ |
$D_4\times C_2$ (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) |
$2$ |
$1$ |
$[2, 2, 3]$ |
$[2, 2, 3]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$ |
$[11, 6, 6, 0]$ |
$[1, 2]$ |
2.8.18.55 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$18$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 2, 3]$ |
$[2, 2, 3]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{3} + 10$ |
$[11, 6, 6, 0]$ |
$[1, 2]$ |
2.8.18.56 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 14$ |
$2$ |
$8$ |
$1$ |
$18$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 2, 3]$ |
$[2, 2, 3]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 14$ |
$[11, 6, 6, 0]$ |
$[1, 2]$ |
2.8.18.7 |
$8$ |
$x^{8} + 4 x^{7} + 22 x^{6} + 52 x^{5} + 137 x^{4} + 192 x^{3} + 220 x^{2} + 132 x + 129$ |
$2$ |
$4$ |
$2$ |
$18$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 6 x^{2} + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
2.8.20.1 |
$8$ |
$x^{8} + 8 x^{7} + 36 x^{6} + 80 x^{5} + 104 x^{4} - 32 x^{3} - 8 x^{2} + 124$ |
$2$ |
$4$ |
$2$ |
$20$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 12\right) x^{2} + 12 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
2.8.20.3 |
$8$ |
$x^{8} + 8 x^{7} + 28 x^{6} + 64 x^{5} + 216 x^{4} + 128 x^{3} + 328 x^{2} + 64 x + 124$ |
$2$ |
$4$ |
$2$ |
$20$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(12 t + 12\right) x^{2} + 8 x + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
2.8.20.5 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 24 x^{5} + 44 x^{4} + 112 x^{3} + 112 x^{2} - 48 x + 36$ |
$2$ |
$4$ |
$2$ |
$20$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(8 t + 8\right) x^{2} + 8 t x + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
2.8.20.8 |
$8$ |
$x^{8} + 12 x^{7} + 78 x^{6} + 308 x^{5} + 795 x^{4} + 1332 x^{3} + 1450 x^{2} + 936 x + 291$ |
$2$ |
$4$ |
$2$ |
$20$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 12 x^{2} + 8 x + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
2.8.22.101 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.22.102 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.22.14 |
$8$ |
$x^{8} + 4 x^{7} + 18 x^{6} + 56 x^{5} + 131 x^{4} + 200 x^{3} + 234 x^{2} + 316 x + 223$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{2} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
2.8.22.16 |
$8$ |
$x^{8} + 8 x^{7} + 72 x^{6} + 48 x^{5} + 108 x^{4} + 176 x^{3} + 176 x^{2} + 224 x + 196$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 8 x + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
2.8.22.19 |
$8$ |
$x^{8} + 16 x^{7} + 60 x^{6} - 40 x^{5} + 96 x^{4} + 544 x^{3} + 40 x^{2} - 144 x + 588$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(12 t + 4\right) x^{2} + 8 t x + 4 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
2.8.22.9 |
$8$ |
$x^{8} + 20 x^{7} + 138 x^{6} + 432 x^{5} + 979 x^{4} + 1632 x^{3} + 1578 x^{2} + 436 x + 223$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
2.8.22.93 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 4 x^{2} + 8 x + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.22.95 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.22.96 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.22.97 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.22.98 |
$8$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 4 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 4 x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.22.99 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.24.17 |
$8$ |
$x^{8} + 14 x^{4} + 12 x^{2} + 8 x + 6$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]^{2}$ |
$t + 1$ |
$x^{8} + 14 x^{4} + 12 x^{2} + 8 x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.24.21 |
$8$ |
$x^{8} + 8 x^{7} + 10 x^{4} + 12 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 10 x^{4} + 12 x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.24.22 |
$8$ |
$x^{8} + 10 x^{4} + 12 x^{2} + 8 x + 18$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]^{2}$ |
$t + 1$ |
$x^{8} + 10 x^{4} + 12 x^{2} + 8 x + 18$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.24.26 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 12 x^{2} + 8 x + 14$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 12 x^{2} + 8 x + 14$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.24.27 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 6$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.24.37 |
$8$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 6$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.24.38 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 30$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 30$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.24.39 |
$8$ |
$x^{8} + 8 x^{7} + 14 x^{4} + 12 x^{2} + 8 x + 30$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 14 x^{4} + 12 x^{2} + 8 x + 30$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |