Defining polynomial
| $x^{5} + b_{19} \pi^{4} x^{4} + a_{18} \pi^{4} x^{3} + b_{22} \pi^{5} x^{2} + b_{21} \pi^{5} x + \pi$ |
Invariants
| Residue field characteristic: | $5$ |
| Degree: | $5$ |
| Base field: | 5.1.5.5a1.3 |
| Ramification index $e$: | $5$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $22$ |
| Absolute Artin slopes: | $[\frac{5}{4},\frac{21}{10}]$ |
| Swan slopes: | $[\frac{9}{2}]$ |
| Means: | $\langle\frac{18}{5}\rangle$ |
| Rams: | $(\frac{9}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $500$ |
| Absolute Mass: | $500$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.