| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.4.8.1 |
$4$ |
$x^{4} + 2 x^{2} + 4 x + 10$ |
$2$ |
$4$ |
$1$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.4.8.2 |
$4$ |
$x^{4} + 2 x^{2} + 4 x + 2$ |
$2$ |
$4$ |
$1$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.4.8.3 |
$4$ |
$x^{4} + 6 x^{2} + 4 x + 14$ |
$2$ |
$4$ |
$1$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{4} + 6 x^{2} + 4 x + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.4.8.4 |
$4$ |
$x^{4} + 6 x^{2} + 4 x + 6$ |
$2$ |
$4$ |
$1$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{4} + 6 x^{2} + 4 x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.4.8.5 |
$4$ |
$x^{4} + 2 x^{2} + 4 x + 6$ |
$2$ |
$4$ |
$1$ |
$8$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.4.8.6 |
$4$ |
$x^{4} + 6 x^{2} + 4 x + 10$ |
$2$ |
$4$ |
$1$ |
$8$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t + 1$ |
$x^{4} + 6 x^{2} + 4 x + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.4.8.7 |
$4$ |
$x^{4} + 4 x^{2} + 4 x + 2$ |
$2$ |
$4$ |
$1$ |
$8$ |
$S_4$ (as 4T5) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{4} + 4 x^{2} + 4 x + 2$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.4.8.8 |
$4$ |
$x^{4} + 4 x + 2$ |
$2$ |
$4$ |
$1$ |
$8$ |
$S_4$ (as 4T5) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{4} + 4 x + 2$ |
$[5, 4, 0]$ |
$[1]$ |
