Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.8.8.2 |
$8$ |
$x^{8} + 8 x^{7} + 56 x^{6} + 240 x^{5} + 816 x^{4} + 2048 x^{3} + 3776 x^{2} + 4928 x + 3760$ |
$2$ |
$2$ |
$4$ |
$8$ |
$C_2^2:C_4$ (as 8T10) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(2 t^{2} + 2 t + 2\right) x + 4 t^{3} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
2.8.12.15 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 12$ |
$2$ |
$4$ |
$2$ |
$12$ |
$C_2^2:C_4$ (as 8T10) |
$4$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{3} + 4 t + 2$ |
$[3, 3, 0]$ |
$[1]$ |
2.8.12.3 |
$8$ |
$x^{8} - 12 x^{7} + 44 x^{6} + 152 x^{5} - 512 x^{4} + 560 x^{3} + 4432 x^{2} + 9376 x + 21744$ |
$2$ |
$2$ |
$4$ |
$12$ |
$C_2^2:C_4$ (as 8T10) |
$4$ |
$1$ |
$[3]$ |
$[2, 3]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + 4 t^{3} x + 4 t^{3} + 12 t + 2$ |
$[2, 0]$ |
$[1]$ |
2.8.16.12 |
$8$ |
$x^{8} + 8 x^{7} + 14 x^{6} - 12 x^{5} + 12 x^{4} + 40 x^{3} + 124 x^{2} + 72 x + 108$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_2^2:C_4$ (as 8T10) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t + 2\right) x^{2} + 4 t x + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.8.16.14 |
$8$ |
$x^{8} + 10 x^{6} - 4 x^{5} + 40 x^{4} - 8 x^{3} + 100 x^{2} + 24 x + 84$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_2^2:C_4$ (as 8T10) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(2 t + 6\right) x^{2} + 4 t x + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.8.16.15 |
$8$ |
$x^{8} + 8 x^{7} + 18 x^{6} + 12 x^{5} + 52 x^{4} + 72 x^{3} + 60 x^{2} + 40 x + 28$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_2^2:C_4$ (as 8T10) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t + 4\right) x^{2} + \left(4 t + 4\right) x + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.8.16.17 |
$8$ |
$x^{8} + 8 x^{7} + 18 x^{6} + 4 x^{5} + 12 x^{4} + 104 x^{3} + 52 x^{2} - 24 x + 156$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_2^2:C_4$ (as 8T10) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t + 2\right) x^{2} + 4 t x + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.8.16.7 |
$8$ |
$x^{8} + 8 x^{5} + 12 x^{4} + 40 x^{2} + 12$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_2^2:C_4$ (as 8T10) |
$4$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 2\right) x^{2} + 4 x + 4 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.8.26.1 |
$8$ |
$x^{8} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.10 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 10$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.11 |
$8$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 26$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 26$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.12 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 26$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 26$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.13 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 18$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 18$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.14 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 10$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.15 |
$8$ |
$x^{8} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 18$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 18$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.16 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{3} + 8 x^{2} + 10$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.2 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 18$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 18$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.3 |
$8$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.4 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.5 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.6 |
$8$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 10$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.7 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 26$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 26$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.8 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.9 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{3} + 8 x^{2} + 26$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2:C_4$ (as 8T10) |
$1$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{3} + 8 x^{2} + 26$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |