Properties

Label 5.1.10.19a2.11-1.4.3a
Base 5.1.10.19a2.11
Degree \(4\)
e \(4\)
f \(1\)
c \(3\)

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Defining polynomial

$x^{4} + d_{0} \pi$

Invariants

Residue field characteristic: $5$
Degree: $4$
Base field: 5.1.10.19a2.11
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $3$
Absolute Artin slopes: $[\frac{9}{4}]$
Swan slopes: $[\ ]$
Means: $\langle\ \rangle$
Rams: $(\ )$
Field count: $0$ (incomplete)
Ambiguity: $4$
Mass: $1$
Absolute Mass: $1$ ($0$ currently in the LMFDB)

The LMFDB does not contain any fields from this family.