Defining polynomial
| $x^{4} + \left(b_{23} \pi^{6} + a_{19} \pi^{5}\right) x^{3} + \left(b_{22} \pi^{6} + b_{18} \pi^{5} + b_{14} \pi^{4}\right) x^{2} + \left(b_{25} \pi^{7} + b_{21} \pi^{6}\right) x + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.31a1.118 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $22$ |
| Absolute Artin slopes: | $[3,4,\frac{55}{12},\frac{55}{12},5]$ |
| Swan slopes: | $[\frac{19}{3},\frac{19}{3}]$ |
| Means: | $\langle\frac{19}{6},\frac{19}{4}\rangle$ |
| Rams: | $(\frac{19}{3},\frac{19}{3})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $64$ |
| Absolute Mass: | $32$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.