Sporadic points on $X_0(N)$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909899305254912 |
|---|---|
| author | Derickx, Maarten Najman, Filip |
| author_facet | Derickx, Maarten Najman, Filip |
| contents | We determine all integers $N$ for which the modular curve $X_0(N)$ admits a sporadic CM point (of any degree), as well as all $N$ for which $X_0(N)$ admits a sporadic point, whether CM or non-CM. In a sense, our results generalize the classification of isogenies of elliptic curves over $\Q$ due to Mazur and Kenku: their work determines the $X_0(N)$ with degree 1 sporadic points, whereas we classify all $X_0(N)$ that have a sporadic point of arbitrary degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09015 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sporadic points on $X_0(N)$ Derickx, Maarten Najman, Filip Number Theory 11G05, 14G05, 11G18 We determine all integers $N$ for which the modular curve $X_0(N)$ admits a sporadic CM point (of any degree), as well as all $N$ for which $X_0(N)$ admits a sporadic point, whether CM or non-CM. In a sense, our results generalize the classification of isogenies of elliptic curves over $\Q$ due to Mazur and Kenku: their work determines the $X_0(N)$ with degree 1 sporadic points, whereas we classify all $X_0(N)$ that have a sporadic point of arbitrary degree. |
| title | Sporadic points on $X_0(N)$ |
| topic | Number Theory 11G05, 14G05, 11G18 |
| url | https://arxiv.org/abs/2511.09015 |