Intermediate modular curves with infinitely many quartic points
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916702233559040 |
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| author | Derickx, Maarten Orlić, Petar |
| author_facet | Derickx, Maarten Orlić, Petar |
| contents | For every group $\{\pm1\}\subseteq Δ\subseteq (\mathbb Z/N\mathbb Z)^\times$, there exists an intermediate modular curve $X_Δ(N)$. In this paper we determine all curves $X_Δ(N)$ with infinitely many points of degree $4$ over $\mathbb Q$. To do that, we developed a method to compute possible degrees of rational morphisms from $X_Δ(N)$ to an elliptic curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intermediate modular curves with infinitely many quartic points Derickx, Maarten Orlić, Petar Number Theory For every group $\{\pm1\}\subseteq Δ\subseteq (\mathbb Z/N\mathbb Z)^\times$, there exists an intermediate modular curve $X_Δ(N)$. In this paper we determine all curves $X_Δ(N)$ with infinitely many points of degree $4$ over $\mathbb Q$. To do that, we developed a method to compute possible degrees of rational morphisms from $X_Δ(N)$ to an elliptic curve. |
| title | Intermediate modular curves with infinitely many quartic points |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.15937 |