Experimental investigations on Lehmer's conjecture for elliptic curves
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911201758281728 |
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| author | Cats, Sven Clark, John Michael Dombrowsky, Charlotte Iranzo, Mar Curco Maughan, Krystal Orvis, Eli |
| author_facet | Cats, Sven Clark, John Michael Dombrowsky, Charlotte Iranzo, Mar Curco Maughan, Krystal Orvis, Eli |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Experimental investigations on Lehmer's conjecture for elliptic curves Cats, Sven Clark, John Michael Dombrowsky, Charlotte Iranzo, Mar Curco Maughan, Krystal Orvis, Eli Number Theory 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. |
| title | Experimental investigations on Lehmer's conjecture for elliptic curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.08871 |