本项目旨在研究模曲线雅可比簇在有理数域的极大阿贝尔扩张中的扭点子群。由Ribeit的一个定理可知，这些群均为有限的。我们将考察其作为Hecke代数模的结构，证明其支集中的理想总是极大Eisenstein理想。进而，我们将考察其与尖点子群之间的关系。

In this project we investigate the torsion subgroups of Jacobian varieties of modular curves over the maximal abelian extension of Q, which are known to be finite by a theorem of Ribet. We will prove that, as Hecke modules, such groups are supported at the maximal Eisenstein ideals. And we will study their relationship between the cuspidal subgroups.