Experimental investigations on Lehmer's conjecture for elliptic curves
Number Theory
2025-10-13 v1
Abstract
In this short note, we give a method for computing a non-torsion point of smallest canonical height on a given elliptic curve 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.
Keywords
Cite
@article{arxiv.2510.08871,
title = {Experimental investigations on Lehmer's conjecture for elliptic curves},
author = {Sven Cats and John Michael Clark and Charlotte Dombrowsky and Mar Curco Iranzo and Krystal Maughan and Eli Orvis},
journal= {arXiv preprint arXiv:2510.08871},
year = {2025}
}
Comments
to appear in Proceedings of LuCaNT II