Empirical Discovery of Rational Points on 5077a1 via Canonical Summation: Correction and Revision in Progress
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2025
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| _version_ | 1866902147420913664 |
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| author | Rice, Christopher David |
| author_facet | Rice, Christopher David |
| contents | <p>We present the empirical discovery of four rational points on the elliptic curve 5077a1 over Q, identified using a canonical height–driven generator-hunting algorithm. These points were originally believed to form a full-rank subgroup of rank 4, exceeding the published rank 3 in both the LMFDB and Cremona tables.</p> <p>Subsequent review confirmed that all four points lie within the Z-span of the known SageMath basis. While the points remain valid and were obtained independently, they do not constitute new generators. This version corrects the earlier misinterpretation of the canonical height matrix rank.</p> <p>All data, coordinates, and verification scripts remain available for transparency and reproducibility. A formal correction notice is included in this version.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15660446 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Empirical Discovery of Rational Points on 5077a1 via Canonical Summation: Correction and Revision in Progress Rice, Christopher David elliptic curves rational points Mordell–Weil group canonical height rank LMFDB SageMath independent generators point finding number theory <p>We present the empirical discovery of four rational points on the elliptic curve 5077a1 over Q, identified using a canonical height–driven generator-hunting algorithm. These points were originally believed to form a full-rank subgroup of rank 4, exceeding the published rank 3 in both the LMFDB and Cremona tables.</p> <p>Subsequent review confirmed that all four points lie within the Z-span of the known SageMath basis. While the points remain valid and were obtained independently, they do not constitute new generators. This version corrects the earlier misinterpretation of the canonical height matrix rank.</p> <p>All data, coordinates, and verification scripts remain available for transparency and reproducibility. A formal correction notice is included in this version.</p> |
| title | Empirical Discovery of Rational Points on 5077a1 via Canonical Summation: Correction and Revision in Progress |
| topic | elliptic curves rational points Mordell–Weil group canonical height rank LMFDB SageMath independent generators point finding number theory |
| url | https://doi.org/10.5281/zenodo.15660446 |