Experimental investigations on Lehmer's conjecture for elliptic curves

2025/10/10 by Cats, Sven, Clark, John Michael, Dombrowsky, Charlotte +3
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.08871

Abstract

In this short note, we give a method for computing a non-torsion point of smallest canonical height on a given elliptic curve E/ℚ over all number fields of a fixed degree. We then describe data collected using this method, and investigate related conjectures of Lehmer and Lang using these data.

Citations

• Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields

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