Computation on Elliptic Curves with Complex Multiplication

Abstract

We give the complete list of possible torsion subgroups of elliptic curves with complex multiplication over number fields of degree 1-13. Additionally we describe the algorithm used to compute these torsion subgroups and its implementation.

24 pages, 3 figures, submitted

References in corpus (1)

• Constructing elliptic curves over finite fields with prescribed torsion

Cited by in corpus (5)

• Torsion points and Galois representations on CM elliptic curves
• Complete classification of the torsion structures of rational elliptic curves over quintic number fields
• A classification of isogeny-torsion graphs of $\mathbb{Q}$-isogeny classes of elliptic curves
• Torsion points and isogenies on CM elliptic curves
• An algorithm for determining torsion growth of elliptic curves