Analysis computes the cuspidal subgroup in modular curves for prime p, suggesting key insights into torsion groups.
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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Elvira Lupoian (2025) studied this question.
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