Properties

Label 3.1.6.11a1.7-1.6.13a
Base 3.1.6.11a1.7
Degree \(6\)
e \(6\)
f \(1\)
c \(13\)

Related objects

Downloads

Learn more

Defining polynomial

$x^{6} + b_{11} \pi^{2} x^{5} + b_{10} \pi^{2} x^{4} + a_{8} \pi^{2} x^{2} + c_{12} \pi^{3} + d_{0} \pi$

Invariants

Residue field characteristic: $3$
Degree: $6$
Base field: 3.1.6.11a1.7
Ramification index $e$: $6$
Residue field degree $f$: $1$
Discriminant exponent $c$: $13$
Absolute Artin slopes: $[2,\frac{5}{2}]$
Swan slopes: $[2]$
Means: $\langle\frac{4}{3}\rangle$
Rams: $(4)$
Field count: $0$ (incomplete)
Ambiguity: $6$
Mass: $18$
Absolute Mass: $6$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.