Consider the monogenic imaginary quadratic field
Sage
K.<α> = QuadraticField(-3)
Discriminant
By Discriminant of an algebraic integer,
Group of units
By ^P1, we have the exceptional case
Class group
Minkowski’s bound is given by
hence
Consider the monogenic imaginary quadratic field
Sage
K.<α> = QuadraticField(-3)
By Discriminant of an algebraic integer,
By ^P1, we have the exceptional case
Minkowski’s bound is given by
hence