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arXiv · 2510.08871

Experimental investigations on Lehmer's conjecture for elliptic curves

Sven Cats·John Michael Clark·Charlotte Dombrowsky·Mar Curco Iranzo·Krystal Maughan·Eli Orvis
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Abstract

In this short note, we give a method for computing a non-torsion point of smallest canonical height on a given elliptic curve $E/\mathbb{Q}$ 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.

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Sven Cats, John Michael Clark, Charlotte Dombrowsky, Mar Curco Iranzo, Krystal Maughan, Eli Orvis. 2025-10-10. Experimental investigations on Lehmer's conjecture for elliptic curves. https://arxiv.org/abs/2510.08871

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