PreprintCC BY 4.0arXiv
Aspects of quadratic Chabauty via modular forms
Abstract
We develop algorithms to construct a basis of de Rham cohomology for modular curves and a matrix representing the Hodge filtration required in the quadratic Chabauty method. We do this without requiring an explicit plane model of the curve and instead compute these objects in terms of modular forms. Our approach works for any modular curve; to demonstrate its efficiency, we implement our method for nonsplit Cartan modular curves.
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BibTeX
@misc{leonhardt2026aspects,
title = {{Aspects of quadratic Chabauty via modular forms}},
author = {Marius Leonhardt and Isabel Rendell},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30703},
eprint = {2610.30703},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30703},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Aspects of quadratic Chabauty via modular forms
AU - Marius Leonhardt
AU - Isabel Rendell
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30703
UR - https://arxiv.org/abs/2610.30703
AB - We develop algorithms to construct a basis of de Rham cohomology for modular curves and a matrix representing the Hodge filtration required in the quadratic Chabauty method. We do this without requiring an explicit plane model of the curve and instead compute these objects in terms of modular forms. Our approach works for any modular curve; to demonstrate its efficiency, we implement our method for nonsplit Cartan modular curves.
ER -