Properties

Label 2.1.24.52i
Base 2.1.1.0a1.1
Degree \(24\)
e \(24\)
f \(1\)
c \(52\)

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Defining polynomial

$x^{24} + 4 b_{47} x^{23} + 4 b_{45} x^{21} + 4 b_{43} x^{19} + 4 b_{41} x^{17} + 2 c_{16} x^{16} + 4 b_{39} x^{15} + 2 b_{14} x^{14} + 4 b_{37} x^{13} + 4 b_{35} x^{11} + 2 a_{10} x^{10} + 4 b_{33} x^{9} + 2 c_{8} x^{8} + 4 b_{31} x^{7} + 4 a_{29} x^{5} + 2 a_{4} x^{4} + 8 c_{48} + 2$

Invariants

Residue field characteristic: $2$
Degree: $24$
Base field: $\Q_{2}$
Ramification index $e$: $24$
Residue field degree $f$: $1$
Discriminant exponent $c$: $52$
Artin slopes: $[\frac{4}{3},\frac{5}{3},3]$
Swan slopes: $[\frac{1}{3},\frac{2}{3},2]$
Means: $\langle\frac{1}{6},\frac{5}{12},\frac{29}{24}\rangle$
Rams: $(1,3,19)$
Field count: $0$ (incomplete)
Ambiguity: $8$
Mass: $1024$
Absolute Mass: $1024$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.