Properties

Label 2.2.16.100l
Base 2.1.1.0a1.1
Degree \(32\)
e \(16\)
f \(2\)
c \(100\)

Related objects

Downloads

Learn more

Defining polynomial over unramified subextension

$x^{16} + 4 b_{30} x^{14} + \left(4 b_{28} + 8 c_{44}\right) x^{12} + 8 b_{43} x^{11} + 4 a_{26} x^{10} + 8 b_{41} x^{9} + 2 a_{8} x^{8} + 8 b_{39} x^{7} + 8 b_{37} x^{5} + 4 b_{20} x^{4} + 8 a_{35} x^{3} + 4 c_{16} + 8 c_{32} + 2$

Invariants

Residue field characteristic: $2$
Degree: $32$
Base field: $\Q_{2}$
Ramification index $e$: $16$
Residue field degree $f$: $2$
Discriminant exponent $c$: $100$
Artin slopes: $[2,3,3,\frac{15}{4}]$
Swan slopes: $[1,2,2,\frac{11}{4}]$
Means: $\langle\frac{1}{2},\frac{5}{4},\frac{13}{8},\frac{35}{16}\rangle$
Rams: $(1,3,3,9)$
Field count: $0$ (incomplete)
Ambiguity: $32$
Mass: $442368$
Absolute Mass: $221184$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.