Properties

Label 2.7.1.0a1.1-1.4.11a
Base 2.7.1.0a1.1
Degree \(4\)
e \(4\)
f \(1\)
c \(11\)

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Defining polynomial

$x^{4} + 8 b_{11} x^{3} + 4 b_{6} x^{2} + 8 b_{9} x + 8 c_{8} + 16 c_{12} + 2$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.7.1.0a1.1
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $11$
Absolute Artin slopes: $[3,4]$
Swan slopes: $[2,3]$
Means: $\langle1,2\rangle$
Rams: $(2,4)$
Field count: $0$ (incomplete)
Ambiguity: $4$
Mass: $2097152$
Absolute Mass: $2097152/7$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.