Defining polynomial over unramified subextension
| $x^{13} + 13 a_{12} x^{12} + 169 c_{13} + 13$ |
Invariants
| Residue field characteristic: | $13$ |
| Degree: | $26$ |
| Base field: | $\Q_{13}$ |
| Ramification index $e$: | $13$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $48$ |
| Artin slopes: | $[2]$ |
| Swan slopes: | $[1]$ |
| Means: | $\langle\frac{12}{13}\rangle$ |
| Rams: | $(1)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $26$ |
| Mass: | $168$ |
| Absolute Mass: | $84$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.