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September 5, 2025Open Access

Computing the Cuspidal Subgroup of the Modular Jacobian J H (p)

Key Points

The computation of the cuspidal subgroup reveals significant structures in modular curves.
This analysis is particularly focused on curves with genus ranging from 2 to 10.
The study compares the cuspidal subgroup to the torsion group of the Jacobian.
Results are based on fixed prime values that are congruent to 1 modulo 4.

Abstract

For a fixed prime p congruent to 1 modulo 4 we define the modular curve X H (p) associated to the subgroup of non-zero squares modulo p. In this paper we compute the cuspidal group for all such curves of genus g, 2≤g≤10 and compare this with the torsion group of the Jacobian J H (ℚ(p)) tors .

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Cite This Study

Elvira Lupoian (Thu,) studied this question.

synapsesocial.com/papers/68bb3ef02b87ece8dc95769e https://doi.org/https://doi.org/10.5802/pmb.63

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