Experimental investigations on Lehmer’s conjecture for elliptic curves
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 E/ \mathbb {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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Cryptography and Residue Arithmetic
Geometry and complex manifolds
Publication details
- Journal / source
- Contemporary mathematics - American Mathematical Society
- Pages
- 111–117
- Publication date
- 1 May 2026
- Language
- EN