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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.08975 |
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| _version_ | 1866915804808740864 |
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| author | Derickx, Maarten Hwang, Wontae Jeon, Daeyeol Orlić, Petar |
| author_facet | Derickx, Maarten Hwang, Wontae Jeon, Daeyeol Orlić, Petar |
| contents | We determine all modular curves $X_0(N)$ with density degree $5$, i.e. all curves $X_0(N)$ with infinitely many points of degree $5$ and only finitely many points of degree $d\leq4$. As a consequence, the problem of determining all curves $X_0(N)$ with infinitely many points of degree $5$ remains open for only $30$ levels $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modular curves $X_0(N)$ of density degree $5$ Derickx, Maarten Hwang, Wontae Jeon, Daeyeol Orlić, Petar Number Theory 11G18, 14G35, 14K02 We determine all modular curves $X_0(N)$ with density degree $5$, i.e. all curves $X_0(N)$ with infinitely many points of degree $5$ and only finitely many points of degree $d\leq4$. As a consequence, the problem of determining all curves $X_0(N)$ with infinitely many points of degree $5$ remains open for only $30$ levels $N$. |
| title | Modular curves $X_0(N)$ of density degree $5$ |
| topic | Number Theory 11G18, 14G35, 14K02 |
| url | https://arxiv.org/abs/2503.08975 |