Defining polynomial over unramified subextension
| $x^{5} + a_{9} \pi^{2} x^{4} + b_{11} \pi^{3} x + \pi$ |
Invariants
| Residue field characteristic: | $5$ |
| Degree: | $10$ |
| Base field: | 5.1.4.3a1.2 |
| Ramification index $e$: | $5$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $26$ |
| Absolute Artin slopes: | $[\frac{25}{16}]$ |
| Swan slopes: | $[\frac{9}{4}]$ |
| Means: | $\langle\frac{9}{5}\rangle$ |
| Rams: | $(\frac{9}{4})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $600$ |
| Absolute Mass: | $75$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.