Torsion points with multiplicatively dependent coordinates on elliptic curves

2019/04/04 by Fabrizio Barroero, Min Sha, Barroero, Fabrizio +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1904.02474

openalex publication_date 2019/04/04 · openalex created_date 2019/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations. In particular, we prove that on an elliptic curve defined over a number field there are only finitely many torsion points whose coordinates are multiplicatively dependent. Moreover, we produce an effective result when the elliptic curve is defined over the rational numbers or has complex multiplication.

Citations

• Torsion points on families of products of elliptic curves

Cited by

• Multiplicative dependence in the denominators of points of elliptic curves

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