Properties

Label 2.2.2.6a1.2-1.8.55a
Base 2.2.2.6a1.2
Degree \(8\)
e \(8\)
f \(1\)
c \(55\)

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Defining polynomial

$x^{8} + \left(b_{63} \pi^{8} + b_{55} \pi^{7}\right) x^{7} + \left(b_{46} \pi^{6} + b_{38} \pi^{5}\right) x^{6} + \left(b_{61} \pi^{8} + b_{53} \pi^{7}\right) x^{5} + \left(b_{28} \pi^{4} + b_{20} \pi^{3}\right) x^{4} + \left(b_{59} \pi^{8} + b_{51} \pi^{7}\right) x^{3} + \left(b_{42} \pi^{6} + b_{34} \pi^{5}\right) x^{2} + \left(b_{57} \pi^{8} + b_{49} \pi^{7}\right) x + c_{64} \pi^{9} + c_{48} \pi^{7} + c_{32} \pi^{5} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $8$
Base field: 2.2.2.6a1.2
Ramification index $e$: $8$
Residue field degree $f$: $1$
Discriminant exponent $c$: $55$
Absolute Artin slopes: $[3,4,5,6]$
Swan slopes: $[4,6,8]$
Means: $\langle2,4,6\rangle$
Rams: $(4,8,16)$
Field count: $0$ (incomplete)
Ambiguity: $8$
Mass: $268435456$
Absolute Mass: $67108864$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.