Experimental investigations on Lehmer’s conjecture for elliptic curves
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Publication date
2026-05
Authors
Cats, Sven
Clark, John Michael
Dombrowsky, Charlotte
Iranzo, Mar Curcó
Maughan, Krystal
Orvis, Eli
Editors
Jones, John W.
Paulhus, Jennifer
Sutherland, Andrew V.
Voight, John
Advisors
Supervisors
Document Type
Part of book
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taverne
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.
Keywords
Taverne, General Mathematics
Citation
Cats, S, Clark, J M, Dombrowsky, C, Iranzo, M C, Maughan, K & Orvis, E 2026, Experimental investigations on Lehmer’s conjecture for elliptic curves. in J W Jones, J Paulhus, A V Sutherland & J Voight (eds), LuCaNT : Databases, Algorithms, and Computational Number Theory - Conference LMFDB, Computation, and Number Theory (LuCaNT) 2025. Contemporary Mathematics, vol. 840, American Mathematical Society, pp. 111-117, Conference on LMFDB, Computation, and Number Theory, LuCaNT 2025, Providence, United States, 7/07/25. https://doi.org/10.1090/conm/840/16810, conference