Properties

Label 2.1.14.22a1.11-1.2.26a
Base 2.1.14.22a1.11
Degree \(2\)
e \(2\)
f \(1\)
c \(26\)

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Defining polynomial

$x^{2} + \left(b_{49} \pi^{25} + b_{47} \pi^{24} + b_{45} \pi^{23} + b_{43} \pi^{22} + b_{41} \pi^{21} + b_{39} \pi^{20} + b_{37} \pi^{19} + b_{35} \pi^{18} + b_{33} \pi^{17} + b_{31} \pi^{16} + b_{29} \pi^{15} + b_{27} \pi^{14} + a_{25} \pi^{13}\right) x + c_{50} \pi^{26} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $2$
Base field: 2.1.14.22a1.11
Ramification index $e$: $2$
Residue field degree $f$: $1$
Discriminant exponent $c$: $26$
Absolute Artin slopes: $[\frac{16}{7},\frac{24}{7}]$
Swan slopes: $[25]$
Means: $\langle\frac{25}{2}\rangle$
Rams: $(25)$
Field count: $0$ (incomplete)
Ambiguity: $2$
Mass: $4096$
Absolute Mass: $2048$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.