Let E be an elliptic curve defined over a number field F. By the Mordell-Weil theorem we know that the points of E with coordinates in F can be given the structure of a finitely generated abelian group. We will focus on the subgroups of points with finite order. For a given prime p > 3 and an elliptic curve E defined over a number field of degree 2p, we would like to know exactly what torsion subgroups arise. Before discussing recent progress on this query, specifically in the case of elliptic curves with complex multiplication (CM), I will provide a brief overview on elliptic curves as well as outline some significant classical results.
Torsion for CM Elliptic Curves Defined Over Number Fields of Degree 2p
Holly Paige Chaos, University of VermontAuthors: Abbey Bourdon and Holly Paige Chaos
2023 AWM Research Symposium
Recent Advances in Curves and Abelian Varieties [Organized by Renee Bell, Padmavathi Srinivasan, and Isabel Vogt]