Defining polynomial
| $x^{5} + a_{3} \pi x^{3} + \pi$ |
Invariants
| Residue field characteristic: | $5$ |
| Degree: | $5$ |
| Base field: | 5.4.2.4a1.2 |
| Ramification index $e$: | $5$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $7$ |
| Absolute Artin slopes: | $[\frac{11}{8}]$ |
| Swan slopes: | $[\frac{3}{4}]$ |
| Means: | $\langle\frac{3}{5}\rangle$ |
| Rams: | $(\frac{3}{4})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $624$ |
| Absolute Mass: | $78$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.