Rational points on elliptic curves

Authors

Keywords:

Diophantine equations, elliptic curves, Heegner points, padic integration, Stark-Heegner points.

Abstract

Elliptic curves are currently among the most extensively studied objects in number theory. They can be described by cubic equations in two variables, but what sets them apart – and makes them fascinating – is the rich algebraic structure exhibited by their solutions. The aim of this article is to explain what elliptic curves are and to explore their most significant properties, some of which rank among the most important results in 20th- and 21st-century mathematics. We will also discuss several open conjectures that continue to shape current research. To place elliptic curves within a broader historical and conceptual context, we present them as a specific class of Diophantine equations – a recurrent and central theme in number theory.

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How to Cite

Guitart, X., & Masdeu, M. (2025). Rational points on elliptic curves. Butlletí De La Societat Catalana De Matemàtiques, 73–102. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/155884

Issue

Vol. 39 Núm. 1-2 (2024)

Section

Articles

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