Properties

Label 2.1.12.24b1.45-1.2.4a
Base 2.1.12.24b1.45
Degree \(2\)
e \(2\)
f \(1\)
c \(4\)

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Defining polynomial

$x^{2} + \left(b_{5} \pi^{3} + a_{3} \pi^{2}\right) x + c_{6} \pi^{4} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $2$
Base field: 2.1.12.24b1.45
Ramification index $e$: $2$
Residue field degree $f$: $1$
Discriminant exponent $c$: $4$
Absolute Artin slopes: $[\frac{4}{3},\frac{5}{3},3]$
Swan slopes: $[3]$
Means: $\langle\frac{3}{2}\rangle$
Rams: $(3)$
Field count: $0$ (incomplete)
Ambiguity: $2$
Mass: $2$
Absolute Mass: $1$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.