| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.4.9.1 |
$4$ |
$x^{4} + 10 x^{2} + 2$ |
$2$ |
$4$ |
$1$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{4} + 10 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.4.9.2 |
$4$ |
$x^{4} + 2 x^{2} + 2$ |
$2$ |
$4$ |
$1$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.4.9.3 |
$4$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$4$ |
$1$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.4.9.4 |
$4$ |
$x^{4} + 10 x^{2} + 8 x + 2$ |
$2$ |
$4$ |
$1$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{4} + 10 x^{2} + 8 x + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.4.9.5 |
$4$ |
$x^{4} + 10 x^{2} + 8 x + 6$ |
$2$ |
$4$ |
$1$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{4} + 10 x^{2} + 8 x + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.4.9.6 |
$4$ |
$x^{4} + 4 x^{3} + 10 x^{2} + 14$ |
$2$ |
$4$ |
$1$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 10 x^{2} + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.4.9.7 |
$4$ |
$x^{4} + 2 x^{2} + 6$ |
$2$ |
$4$ |
$1$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.4.9.8 |
$4$ |
$x^{4} + 10 x^{2} + 6$ |
$2$ |
$4$ |
$1$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{4} + 10 x^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
