A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring

Sala, Massimiliano and Taufer, Daniele
(2022) A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring.
International Journal of Group Theory. ISSN 2251-7669
(In Press)

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Abstract

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 provided, and open questions regarding the structure of their points are highlighted.

Item Type: Article
Divisions: Antoine Joux (AJ)
Depositing User: Daniele Taufer
Date Deposited: 08 Jul 2022 09:47
Last Modified: 08 Jul 2022 09:47
Primary Research Area: NRA3: Threat Detection and Defenses
URI: https://publications.cispa.saarland/id/eprint/3720

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