Properties

Label 2.1.28.46b
Base 2.1.1.0a1.1
Degree \(28\)
e \(28\)
f \(1\)
c \(46\)

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Defining polynomial

$x^{28} + 2 b_{27} x^{27} + 2 b_{25} x^{25} + 2 b_{23} x^{23} + 2 b_{21} x^{21} + 2 a_{19} x^{19} + 4 c_{36} x^{8} + 4 b_{35} x^{7} + 4 b_{33} x^{5} + 2 c_{4} x^{4} + 4 b_{31} x^{3} + 2 a_{2} x^{2} + 4 b_{29} x + 2$

Invariants

Residue field characteristic: $2$
Degree: $28$
Base field: $\Q_{2}$
Ramification index $e$: $28$
Residue field degree $f$: $1$
Discriminant exponent $c$: $46$
Artin slopes: $[\frac{8}{7},\frac{16}{7}]$
Swan slopes: $[\frac{1}{7},\frac{9}{7}]$
Means: $\langle\frac{1}{14},\frac{19}{28}\rangle$
Rams: $(1,17)$
Field count: $0$ (incomplete)
Ambiguity: $4$
Mass: $256$
Absolute Mass: $256$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.