The results below are complete, since the LMFDB contains all p-adic fields of degree at most 23 and residue characteristic at most 199
| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 2.1.2.2a1.1 |
$2$ |
$x^{2} + 2 x + 2$ |
$2$ |
$1$ |
$2$ |
$2$ |
$C_2$ (as 2T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 1$ |
$x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 2]$ |
| 2.1.2.2a1.2 |
$2$ |
$x^{2} + 2 x + 6$ |
$2$ |
$1$ |
$2$ |
$2$ |
$C_2$ (as 2T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 1$ |
$x^{2} + 2 x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 4]$ |
| 2.1.2.3a1.1 |
$2$ |
$x^{2} + 2$ |
$2$ |
$1$ |
$2$ |
$3$ |
$C_2$ (as 2T1) |
$1$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]$ |
$[2]$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 1$ |
$x^{2} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.1.2.3a1.2 |
$2$ |
$x^{2} + 10$ |
$2$ |
$1$ |
$2$ |
$3$ |
$C_2$ (as 2T1) |
$1$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]$ |
$[2]$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 1$ |
$x^{2} + 10$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.1.2.3a1.3 |
$2$ |
$x^{2} + 4 x + 2$ |
$2$ |
$1$ |
$2$ |
$3$ |
$C_2$ (as 2T1) |
$1$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]$ |
$[2]$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 1$ |
$x^{2} + 4 x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.1.2.3a1.4 |
$2$ |
$x^{2} + 4 x + 10$ |
$2$ |
$1$ |
$2$ |
$3$ |
$C_2$ (as 2T1) |
$1$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]$ |
$[2]$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 1$ |
$x^{2} + 4 x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
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