Rational points on a certain genus 2 curve
We give a correct proof to the fact that all rational points on the curve \[ y^2=(x^2+1)(x^2+3)(x^2+7) \] are $\pm \infty $ and $(\pm 1,\,\pm 8)$. This corrects previous works of Cohen [3] and Duquesne [4, 5].
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.471/ |
| _version_ | 1797651488829341696 |
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| author | Nguyen, Xuan Tho |
| author_facet | Nguyen, Xuan Tho |
| author_sort | Nguyen, Xuan Tho |
| collection | DOAJ |
| description | We give a correct proof to the fact that all rational points on the curve
\[ y^2=(x^2+1)(x^2+3)(x^2+7) \]
are $\pm \infty $ and $(\pm 1,\,\pm 8)$. This corrects previous works of Cohen [3] and Duquesne [4, 5]. |
| first_indexed | 2024-03-11T16:16:32Z |
| format | Article |
| id | doaj.art-a895e33bceb14e4a85b90b9f0bf6e2f9 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:32Z |
| publishDate | 2023-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-a895e33bceb14e4a85b90b9f0bf6e2f92023-10-24T14:20:39ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-09-01361G61071107310.5802/crmath.47110.5802/crmath.471Rational points on a certain genus 2 curveNguyen, Xuan Tho0Hanoi University of Science and TechnologyWe give a correct proof to the fact that all rational points on the curve \[ y^2=(x^2+1)(x^2+3)(x^2+7) \] are $\pm \infty $ and $(\pm 1,\,\pm 8)$. This corrects previous works of Cohen [3] and Duquesne [4, 5].https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.471/ |
| spellingShingle | Nguyen, Xuan Tho Rational points on a certain genus 2 curve Comptes Rendus. Mathématique |
| title | Rational points on a certain genus 2 curve |
| title_full | Rational points on a certain genus 2 curve |
| title_fullStr | Rational points on a certain genus 2 curve |
| title_full_unstemmed | Rational points on a certain genus 2 curve |
| title_short | Rational points on a certain genus 2 curve |
| title_sort | rational points on a certain genus 2 curve |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.471/ |
| work_keys_str_mv | AT nguyenxuantho rationalpointsonacertaingenus2curve |