2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72630We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized algorithm can be adapted to yield the discriminant of the endomorphism ring of the curve.13 pages, 2 tables, 1 appendixNumber Theory11G05; 11G15text