Torsion growth over cubic fields of rational elliptic curves with complex multiplication

This article is a contribution to the project of classifying the torsion growth of elliptic curves upon base-change. In this article, we treat the case of elliptic curves defined over the rationals with complex multiplication. For this particular case, we give a description of the possible torsion growth over cubic fields, and a completely explicit description of this growth in terms of some invariants attached to a given elliptic curve.