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Label |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
Slope content |
5.8.0.1 |
x8 + x2 - 2x + 3 |
$5$ |
$1$ |
$8$ |
$0$ |
$C_8$ (as 8T1) |
$ [\ ]^{8}$ |
5.8.4.1 |
x8 + 10x6 + 125x4 + 2500 |
$5$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$ [\ ]_{2}^{4}$ |
5.8.4.2 |
x8 + 25x4 - 250x2 + 1250 |
$5$ |
$2$ |
$4$ |
$4$ |
$C_8$ (as 8T1) |
$ [\ ]_{2}^{4}$ |
5.8.6.1 |
x8 - 5x4 + 400 |
$5$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$ [\ ]_{4}^{2}$ |
5.8.6.2 |
x8 + 15x4 + 100 |
$5$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$ [\ ]_{4}^{2}$ |
5.8.6.3 |
x8 + 25x4 + 200 |
$5$ |
$4$ |
$2$ |
$6$ |
$C_8$ (as 8T1) |
$ [\ ]_{4}^{2}$ |
5.8.6.4 |
x8 - 5x4 + 50 |
$5$ |
$4$ |
$2$ |
$6$ |
$C_8$ (as 8T1) |
$ [\ ]_{4}^{2}$ |
5.8.7.1 |
x8 - 5 |
$5$ |
$8$ |
$1$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$ [\ ]_{8}^{2}$ |
5.8.7.2 |
x8 - 20 |
$5$ |
$8$ |
$1$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$ [\ ]_{8}^{2}$ |
5.8.7.3 |
x8 + 10 |
$5$ |
$8$ |
$1$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$ [\ ]_{8}^{2}$ |
5.8.7.4 |
x8 + 40 |
$5$ |
$8$ |
$1$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$ [\ ]_{8}^{2}$ |
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