Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913893213798400 |
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| author | Gajović, Stevan Hanselman, Jeroen Koutsianas, Angelos |
| author_facet | Gajović, Stevan Hanselman, Jeroen Koutsianas, Angelos |
| contents | In this paper, we prove that the local-global principle of $11$-isogenies for elliptic curves over quadratic fields does not fail. This gives a positive answer to a conjecture by Banwait and Cremona. The proof is based on the determination of the set of quadratic points on the modular curve $X_{D_{10}}(11)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields Gajović, Stevan Hanselman, Jeroen Koutsianas, Angelos Number Theory Primary 14G05, 11G18, Secondary 11G05 In this paper, we prove that the local-global principle of $11$-isogenies for elliptic curves over quadratic fields does not fail. This gives a positive answer to a conjecture by Banwait and Cremona. The proof is based on the determination of the set of quadratic points on the modular curve $X_{D_{10}}(11)$. |
| title | Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields |
| topic | Number Theory Primary 14G05, 11G18, Secondary 11G05 |
| url | https://arxiv.org/abs/2501.17602 |