There are infinitely many elliptic curves over the rationals of rank 2
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913676630425600 |
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| author | Zywina, David |
| author_facet | Zywina, David |
| contents | We show that there are infinitely many elliptic curves $E/\mathbb{Q}$, up to isomorphism over $\overline{\mathbb{Q}}$, for which the finitely generated group $E(\mathbb{Q})$ has rank exactly $2$. Our elliptic curves are given by explicit models and their rank is shown to be $2$ via a $2$-descent. That there are infinitely many such elliptic curves makes use of a theorem of Tao and Ziegler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | There are infinitely many elliptic curves over the rationals of rank 2 Zywina, David Number Theory 11G18 (Primary) 14J27 (Secondary) We show that there are infinitely many elliptic curves $E/\mathbb{Q}$, up to isomorphism over $\overline{\mathbb{Q}}$, for which the finitely generated group $E(\mathbb{Q})$ has rank exactly $2$. Our elliptic curves are given by explicit models and their rank is shown to be $2$ via a $2$-descent. That there are infinitely many such elliptic curves makes use of a theorem of Tao and Ziegler. |
| title | There are infinitely many elliptic curves over the rationals of rank 2 |
| topic | Number Theory 11G18 (Primary) 14J27 (Secondary) |
| url | https://arxiv.org/abs/2502.01957 |