Detecting complex multiplication

Abstract

We give an efficient, deterministic algorithm to decide if two abelian varieties over a number field are isogenous. From this, we derive an algorithm to compute the endomorphism ring of an elliptic curve over a number field.

Cited by in corpus (3)

• Reductions of points on algebraic groups
• Computing the endomorphism ring of an elliptic curve over a number field
• On the paramodularity of typical abelian surfaces (and reduction of G-covariant bilinear forms)