Imaginary quadratic field

Consider the monogenic imaginary quadratic field where . #m/thm/num/alg

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 is trivial, i.e. is a UFD.

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