Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.8.8.12 |
$8$ |
$x^{8} - 2 x^{6} - 2 x^{5} + 8 x^{4} + 8 x^{3} - 4 x + 4$ |
$2$ |
$4$ |
$2$ |
$8$ |
$A_4\wr C_2$ (as 8T42) |
$6$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 t x^{2} + 2 t x + 2$ |
$[1, 1, 0]$ |
$[1]$ |
2.8.16.25 |
$8$ |
$x^{8} - 4 x^{5} + 8 x^{4} + 16 x^{2} + 8 x + 28$ |
$2$ |
$4$ |
$2$ |
$16$ |
$A_4\wr C_2$ (as 8T42) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x + 4 t + 6$ |
$[5, 4, 0]$ |
$[1]$ |
2.8.16.26 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 36 x^{5} + 44 x^{4} + 64 x^{3} + 64 x^{2} + 24 x + 36$ |
$2$ |
$4$ |
$2$ |
$16$ |
$A_4\wr C_2$ (as 8T42) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 4 x^{2} + \left(4 t + 4\right) x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
2.8.16.27 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} - 20 x^{5} + 12 x^{4} + 80 x^{3} - 8 x^{2} - 24 x + 36$ |
$2$ |
$4$ |
$2$ |
$16$ |
$A_4\wr C_2$ (as 8T42) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 4 t x^{2} + 4 t x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
2.8.16.28 |
$8$ |
$x^{8} - 4 x^{5} + 16 x^{2} + 24 x + 12$ |
$2$ |
$4$ |
$2$ |
$16$ |
$A_4\wr C_2$ (as 8T42) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x + 4 t + 2$ |
$[5, 4, 0]$ |
$[1]$ |