English

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 E/QE/\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.

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