Properties

Label 2.3.2.9a1.6-1.6.17a
Base 2.3.2.9a1.6
Degree \(6\)
e \(6\)
f \(1\)
c \(17\)

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Defining polynomial

$x^{6} + \left(b_{23} \pi^{4} + b_{17} \pi^{3}\right) x^{5} + \left(b_{21} \pi^{4} + b_{15} \pi^{3}\right) x^{3} + \left(b_{19} \pi^{4} + b_{13} \pi^{3}\right) x + c_{24} \pi^{5} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $6$
Base field: 2.3.2.9a1.6
Ramification index $e$: $6$
Residue field degree $f$: $1$
Discriminant exponent $c$: $17$
Absolute Artin slopes: $[3,4]$
Swan slopes: $[4]$
Means: $\langle2\rangle$
Rams: $(12)$
Field count: $0$ (incomplete)
Ambiguity: $2$
Mass: $262144$
Absolute Mass: $131072/3$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.