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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/2505.10777 |
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Table of Contents:
- Let \( p \geq 5 \) be a prime. In 2003 Conrad, Edixhoven, and Stein conjectured that the rational torsion subgroup of the modular Jacobian \( J_1(p) \) coincides with the rational cuspidal divisor class group. Using explicit computations in Magma, the open case \( p = 29 \) has been proven by Derickx, Kamienny, Stein, and Stoll in 2023. We extend these results to primes \( p = 97, 101, 109, \) and \( 113 \). In addition, we provide a list of the groups \( J_1(p)(\mathbb{Q})_{\text{tors}} \) for every prime up to \( p \leq 113 \). However, our method is general and can be applied to larger primes.