Properties

Label 2.1.8.27a1.36-1.4.56b
Base 2.1.8.27a1.36
Degree \(4\)
e \(4\)
f \(1\)
c \(56\)

Related objects

Downloads

Learn more

Defining polynomial

$x^{4} + \left(b_{79} \pi^{20} + b_{75} \pi^{19} + b_{71} \pi^{18} + b_{67} \pi^{17} + b_{63} \pi^{16} + b_{59} \pi^{15} + b_{55} \pi^{14}\right) x^{3} + \left(b_{50} \pi^{13} + b_{46} \pi^{12} + b_{42} \pi^{11} + b_{38} \pi^{10} + b_{34} \pi^{9} + b_{30} \pi^{8} + a_{26} \pi^{7}\right) x^{2} + \left(b_{77} \pi^{20} + b_{73} \pi^{19} + b_{69} \pi^{18} + b_{65} \pi^{17} + b_{61} \pi^{16} + b_{57} \pi^{15} + a_{53} \pi^{14}\right) x + c_{80} \pi^{21} + c_{52} \pi^{14} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.8.27a1.36
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $56$
Absolute Artin slopes: $[2,\frac{7}{2},\frac{9}{2},\frac{41}{8},6]$
Swan slopes: $[13,20]$
Means: $\langle\frac{13}{2},\frac{53}{4}\rangle$
Rams: $(13,27)$
Field count: $0$ (incomplete)
Ambiguity: $4$
Mass: $524288$
Absolute Mass: $262144$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.