This article is a contribution to the project of classifying the torsion growth of elliptic curve upon base-change. In this article we treat the case of elliptic curve 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.
Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields
The theory of complex multiplication for K3 surfaces
On the periods of motives with complex multiplication and a conjecture of Gross-Deligne
![QR code for arXiv:1909.00634 [math.NT]](http://oss.arxitics.com/images/favicon.svg)