Determining the rational points on a curve of genus 2 and Mordell-Weil rank 1
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915521752989696 |
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| author | Stoll, Michael |
| author_facet | Stoll, Michael |
| contents | We explain how one can efficiently determine the (finite) set of rational points on a curve of genus 2 over $\mathbb Q$ with Jacobian variety $J$, given a point $P \in J(\mathbb Q)$ generating a subgroup of finite index in $J(\mathbb Q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24604 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determining the rational points on a curve of genus 2 and Mordell-Weil rank 1 Stoll, Michael Number Theory Algebraic Geometry 11G30, 11D41, 14G05, 11Y50, 11-04, 11G10, 14G25, 14H25, 14H40, 14Q05 We explain how one can efficiently determine the (finite) set of rational points on a curve of genus 2 over $\mathbb Q$ with Jacobian variety $J$, given a point $P \in J(\mathbb Q)$ generating a subgroup of finite index in $J(\mathbb Q)$. |
| title | Determining the rational points on a curve of genus 2 and Mordell-Weil rank 1 |
| topic | Number Theory Algebraic Geometry 11G30, 11D41, 14G05, 11Y50, 11-04, 11G10, 14G25, 14H25, 14H40, 14Q05 |
| url | https://arxiv.org/abs/2509.24604 |