Properties

Label 2.1.8.24c1.11-1.4.46e
Base 2.1.8.24c1.11
Degree \(4\)
e \(4\)
f \(1\)
c \(46\)

Related objects

Downloads

Learn more

Defining polynomial

$x^{4} + \left(b_{59} \pi^{15} + b_{55} \pi^{14} + b_{51} \pi^{13} + b_{47} \pi^{12} + a_{43} \pi^{11}\right) x^{3} + \left(b_{50} \pi^{13} + b_{46} \pi^{12} + b_{42} \pi^{11} + b_{38} \pi^{10} + b_{34} \pi^{9} + b_{30} \pi^{8} + a_{26} \pi^{7}\right) x^{2} + \left(b_{57} \pi^{15} + b_{53} \pi^{14} + b_{49} \pi^{13} + b_{45} \pi^{12}\right) x + c_{60} \pi^{16} + c_{52} \pi^{14} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.8.24c1.11
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $46$
Absolute Artin slopes: $[2,3,4,\frac{19}{4},5]$
Swan slopes: $[13,15]$
Means: $\langle\frac{13}{2},\frac{43}{4}\rangle$
Rams: $(13,17)$
Field count: $0$ (incomplete)
Ambiguity: $4$
Mass: $16384$
Absolute Mass: $4096$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.