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: | 2.1.8.31a1.149 |
Ramification index $e$: | $4$ |
Residue field degree $f$: | $1$ |
Discriminant exponent $c$: | $20$ |
Absolute Artin slopes: | $[3,4,\frac{53}{12},\frac{53}{12},5]$ |
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: | $8$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.