Properties

Label 2.1.8.31a1.149-1.4.20a
Base 2.1.8.31a1.149
Degree \(4\)
e \(4\)
f \(1\)
c \(20\)

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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.