Some remarks on the construction of class polynomials
Elisavet Konstantinou, Aristides Kontogeorgis · Advances in Mathematics of Communications · 2011
Class invariants are singular values of modular functions which generate the class fields ofimaginary quadratic number fields. Their minimal polynomials, called class polynomials, are uniquelydetermined by a discriminant $-D<0$ and are used in many applications, including the generation of ellipticcurves. In all these applications, it is desirable that the size of the polynomials is as small as possible.Among all known class polynomials, Weber polynomials constructed with discriminants $-D \equiv 1$ (mod $8$) have thesmallest height and require the least precision for their construction. In this paper, we will show thatthis fact does not necessarily lead to the most efficient computations, since the congruences modulo $8$ ofthe discriminants affect the degrees of the polynomials.