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Computing the Cuspidal Subgroup of the Modular Jacobian $J_{H}(p)$
Elvira Lupoian1
1Department of Mathematics, University College London, London, United Kingdom
Publications mathématiques de Besançon. Algèbre et théorie des nombres (2025), pp. 97-113

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 $g$, $2 \le g \le 10$ and compare this with the torsion group of the Jacobian $J_{H}(\mathbb{Q}(\sqrt{p} ))_{\mathrm{tors}}$.

Soit p un nombre premier, égal à $1 \bmod 4$, et $X_{H}(p)$ la courbe modulaire correspondant au groupe des carrés $\bmod \ p$. Dans cet article, nous calculons le groupe cuspidal de $X_{H}(p)$ et le comparons au groupe de torsion de la Jacobienne $J_{H}(p)(\mathbb{Q}(\sqrt{p})_{\mathrm{tors}}$.

Published online:
DOI: 10.5802/pmb.63
Classification: 11Y99, 11G10
Keywords: Modular Jacobians, Cuspidal Subgroup

Elvira Lupoian  1

1 Department of Mathematics, University College London, London, United Kingdom
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Elvira Lupoian. Computing the Cuspidal Subgroup of the Modular Jacobian $J_{H}(p)$. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2025), pp. 97-113. doi: 10.5802/pmb.63
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     title = {Computing the {Cuspidal} {Subgroup} of the {Modular} {Jacobian} $J_{H}(p)$},
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     year = {2025},
     publisher = {Presses universitaires de Franche-Comt\'e},
     doi = {10.5802/pmb.63},
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