Properties

Label 2.3.2.9a1.6-1.4.8b
Base 2.3.2.9a1.6
Degree \(4\)
e \(4\)
f \(1\)
c \(8\)

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Defining polynomial

$x^{4} + b_{7} \pi^{2} x^{3} + a_{2} \pi x^{2} + a_{5} \pi^{2} x + c_{8} \pi^{3} + c_{4} \pi^{2} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.3.2.9a1.6
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $8$
Absolute Artin slopes: $[2,3,3]$
Swan slopes: $[1,2]$
Means: $\langle\frac{1}{2},\frac{5}{4}\rangle$
Rams: $(1,3)$
Field count: $0$ (incomplete)
Ambiguity: $4$
Mass: $392$
Absolute Mass: $196/3$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.