Properties

Label 2.1.14.26a1.33-1.2.29a
Base 2.1.14.26a1.33
Degree \(2\)
e \(2\)
f \(1\)
c \(29\)

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Defining polynomial

$x^{2} + \left(b_{55} \pi^{28} + b_{53} \pi^{27} + b_{51} \pi^{26} + b_{49} \pi^{25} + b_{47} \pi^{24} + b_{45} \pi^{23} + b_{43} \pi^{22} + b_{41} \pi^{21} + b_{39} \pi^{20} + b_{37} \pi^{19} + b_{35} \pi^{18} + b_{33} \pi^{17} + b_{31} \pi^{16} + b_{29} \pi^{15}\right) x + c_{56} \pi^{29} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $2$
Base field: 2.1.14.26a1.33
Ramification index $e$: $2$
Residue field degree $f$: $1$
Discriminant exponent $c$: $29$
Absolute Artin slopes: $[\frac{20}{7},\frac{55}{14}]$
Swan slopes: $[28]$
Means: $\langle14\rangle$
Rams: $(28)$
Field count: $0$ (incomplete)
Ambiguity: $2$
Mass: $16384$
Absolute Mass: $8192$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.