We give an algorithm to compute the generalized division polynomials for elliptic curves with complex multiplication. These polynomials can be used to generate the ray class fields of imaginary quadratic fields over the Hilbert class field with no restriction on the conductor.
Complex multiplication, division polynomial, Hurwitz number
"On the computation of generalized division polynomials,"
Turkish Journal of Mathematics: Vol. 39:
4, Article 10.
Available at: https://journals.tubitak.gov.tr/math/vol39/iss4/10