| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.4.11.1 |
$4$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$2$ |
$4$ |
$1$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[3, 4]$ |
$t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.10 |
$4$ |
$x^{4} + 4 x^{2} + 26$ |
$2$ |
$4$ |
$1$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[3, 4]$ |
$t + 1$ |
$x^{4} + 4 x^{2} + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.11 |
$4$ |
$x^{4} + 10$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{4} + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.12 |
$4$ |
$x^{4} + 26$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{4} + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.13 |
$4$ |
$x^{4} + 8 x^{3} + 8 x + 10$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t + 1$ |
$x^{4} + 8 x^{3} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.14 |
$4$ |
$x^{4} + 8 x + 10$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t + 1$ |
$x^{4} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.15 |
$4$ |
$x^{4} + 12 x^{2} + 8 x + 2$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{4} + 12 x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.16 |
$4$ |
$x^{4} + 12 x^{2} + 8 x + 18$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{4} + 12 x^{2} + 8 x + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.17 |
$4$ |
$x^{4} + 8 x^{3} + 8 x + 2$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t + 1$ |
$x^{4} + 8 x^{3} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.18 |
$4$ |
$x^{4} + 8 x + 18$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t + 1$ |
$x^{4} + 8 x + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.19 |
$4$ |
$x^{4} + 12 x^{2} + 8 x + 26$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{4} + 12 x^{2} + 8 x + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.2 |
$4$ |
$x^{4} + 4 x^{2} + 2$ |
$2$ |
$4$ |
$1$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[3, 4]$ |
$t + 1$ |
$x^{4} + 4 x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.20 |
$4$ |
$x^{4} + 12 x^{2} + 8 x + 10$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{4} + 12 x^{2} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.3 |
$4$ |
$x^{4} + 4 x^{2} + 18$ |
$2$ |
$4$ |
$1$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[3, 4]$ |
$t + 1$ |
$x^{4} + 4 x^{2} + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.4 |
$4$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 18$ |
$2$ |
$4$ |
$1$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[3, 4]$ |
$t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.5 |
$4$ |
$x^{4} + 2$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{4} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.6 |
$4$ |
$x^{4} + 18$ |
$2$ |
$4$ |
$1$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{4} + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.7 |
$4$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 26$ |
$2$ |
$4$ |
$1$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[3, 4]$ |
$t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.8 |
$4$ |
$x^{4} + 4 x^{2} + 10$ |
$2$ |
$4$ |
$1$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[3, 4]$ |
$t + 1$ |
$x^{4} + 4 x^{2} + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.4.11.9 |
$4$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$2$ |
$4$ |
$1$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[3, 4]$ |
$t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
