Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.8.12.20 |
$8$ |
$x^{8} - 2 x^{7} + 2 x^{6} + 8 x^{5} + 8 x^{4} - 4 x^{3} - 4 x^{2} + 4$ |
$2$ |
$4$ |
$2$ |
$12$ |
$C_2^3: C_4$ (as 8T21) |
$4$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 t x^{3} + 2 t x^{2} + 2$ |
$[3, 2, 0]$ |
$[2]$ |
2.8.16.30 |
$8$ |
$x^{8} - 4 x^{7} + 28 x^{6} - 16 x^{5} + 24 x^{4} + 88 x^{3} + 40 x^{2} + 16 x + 52$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_2^3: C_4$ (as 8T21) |
$4$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 6 x^{2} + 4 x + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.8.16.39 |
$8$ |
$x^{8} + 4 x^{6} - 4 x^{5} + 32 x^{4} - 8 x^{3} + 72 x^{2} - 56 x + 196$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_2^3: C_4$ (as 8T21) |
$4$ |
$1$ |
$[2, 3]$ |
$[2, 3, 3]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{2} + 4 t x + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.8.16.40 |
$8$ |
$x^{8} + 8 x^{6} - 4 x^{5} + 56 x^{4} + 8 x^{3} + 128 x^{2} - 56 x + 196$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_2^3: C_4$ (as 8T21) |
$4$ |
$1$ |
$[2, 3]$ |
$[2, 3, 3]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 6\right) x^{2} + 4 t x + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
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) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(8 t + 14\right) x^{2} + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
2.8.18.20 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 40 x^{4} + 64 x^{3} + 160 x^{2} + 96 x + 84$ |
$2$ |
$4$ |
$2$ |
$18$ |
$C_2^3: C_4$ (as 8T21) |
$2$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 6\right) x^{2} + 8 x + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
2.8.25.1 |
$8$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 16 x + 2$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 16 x + 2$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.2 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 14 x^{4} + 8 x^{3} + 28 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 14 x^{4} + 8 x^{3} + 28 x^{2} + 2$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.3 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 2$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.33 |
$8$ |
$x^{8} + 2 x^{4} + 20 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 20 x^{2} + 10$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.34 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 20 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 20 x^{2} + 10$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.35 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 10$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.36 |
$8$ |
$x^{8} + 4 x^{6} + 6 x^{4} + 8 x^{3} + 28 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 6 x^{4} + 8 x^{3} + 28 x^{2} + 10$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.37 |
$8$ |
$x^{8} + 4 x^{6} + 6 x^{4} + 8 x^{3} + 12 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 6 x^{4} + 8 x^{3} + 12 x^{2} + 10$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.38 |
$8$ |
$x^{8} + 2 x^{4} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x^{2} + 10$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.39 |
$8$ |
$x^{8} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 16 x + 10$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 16 x + 10$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.4 |
$8$ |
$x^{8} + 2 x^{4} + 20 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 20 x^{2} + 2$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.40 |
$8$ |
$x^{8} + 2 x^{4} + 20 x^{2} + 16 x + 10$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 20 x^{2} + 16 x + 10$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.5 |
$8$ |
$x^{8} + 2 x^{4} + 4 x^{2} + 16 x + 2$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x^{2} + 16 x + 2$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.6 |
$8$ |
$x^{8} + 2 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x^{2} + 2$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.7 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 20 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 20 x^{2} + 2$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.25.8 |
$8$ |
$x^{8} + 2 x^{4} + 20 x^{2} + 16 x + 2$ |
$2$ |
$8$ |
$1$ |
$25$ |
$C_2^3: C_4$ (as 8T21) |
$1$ |
$1$ |
$[2, 3, 17/4]$ |
$[2, 3, 7/2, 4, 17/4]$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 20 x^{2} + 16 x + 2$ |
$[18, 10, 4, 0]$ |
$[1, 1, 1]$ |