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

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posted on 2023-11-29, 18:05 authored by Massimiliano Sala, Daniele Taufer
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.

History

Preferred Citation

Massimiliano Sala and Daniele Taufer. A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring. In: International Journal of Group Theory. 2022.

Primary Research Area

  • Algorithmic Foundations and Cryptography

Legacy Posted Date

2022-07-08

Journal

International Journal of Group Theory

Open Access Type

  • Gold

Sub Type

  • Article

BibTeX

@article{cispa_all_3720, title = "A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring", author = "Sala, Massimiliano and Taufer, Daniele", journal="{International Journal of Group Theory}", year="2022", }

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