Defining polynomial
| $x^{4} + b_{19} \pi^{5} x^{3} + \left(b_{22} \pi^{6} + b_{18} \pi^{5} + b_{14} \pi^{4}\right) x^{2} + \left(b_{21} \pi^{6} + a_{17} \pi^{5}\right) x + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.7.6a1.1 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $20$ |
| Absolute Artin slopes: | $[\frac{38}{21},\frac{38}{21}]$ |
| Swan slopes: | $[\frac{17}{3},\frac{17}{3}]$ |
| Means: | $\langle\frac{17}{6},\frac{17}{4}\rangle$ |
| Rams: | $(\frac{17}{3},\frac{17}{3})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $32$ |
| Absolute Mass: | $32$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.