Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields

2011/11/10 by Graeme Taylor, Taylor, Graeme · 1 citation
Mathematics · Social Sciences · #14H52 #Algebraic Geometry (math.AG) #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1111.2475

openalex publication_date 2011/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give examples of points with particularly low height on elliptic curves over quadratic fields, recovered by a search over elliptic divisibility sequences. The smallest example identified satisfies dh(P)=0.0077127...: improving on the previous smallest for curves over quadratic fields of dh(P)=0.0194426... given by Everest and Ward; and comparable with some of the examples of smallest height on curves over Q tabulated by Elkies.

Cited by

• Experimental investigations on Lehmer's conjecture for elliptic curves

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