Detecting complex multiplication

Jeffrey D. Achter
2005 Computational Aspects of Algebraic Curves  
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.
doi:10.1142/9789812701640_0003 fatcat:guvuq35k3bfmnpn2sfkewcpfv4