Imaginary quadratic field Consider the monogenic imaginary quadratic field where . alg Sage K.<α> = QuadraticField(-14) Discriminant By Discriminant of an algebraic integer, Group of units By ^P1, Class group Minkowski’s bound is given by so applying Kummer’s factorization theorem norms Clearly no algebraic integers can have these norms, so we can be satisfied that these are not principal. Since , the ideal class group is generated by . Some algebraic integers of small field norm are from which we derive the relation whence , so . Therefore tidy | en | sembr