University of Isfahan International Journal of Group Theory 2251-7650 12 3 2023 09 01 A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring 177 196 26665 10.22108/ijgt.2022.131984.1769 EN Massimiliano Sala Department of Mathematics, University of Trento, Trento, Italy Daniele Taufer CISPA, Helmholtz Center for Information Security, Saarbrücken, Germany Journal Article 2021 12 23 We survey the known group structures arising from elliptic curves defined by Weierstrass models over commutative rings with unity and satisfying a technical condition. For every considered base ring, the groups that may arise depending on the curve coefficients are recalled. When a complete classification is still out of reach, partial results about the group structure and relevant subgroups are provided. Several examples of elliptic curves over the inspected rings are presented, and open questions regarding the structure of their points are highlighted. Elliptic curves group of points effective addition law https://ijgt.ui.ac.ir/article_26665_eef610da29551cc3b348a913071109b3.pdf