Quadratic Chabauty for modular curves: algorithms and examples

DOI10.1112/S0010437X23007170zbMATH Open1529.11080arXiv2101.01862OpenAlexW3121046320MaRDI QIDQ6044854

Author name not available (Why is that?)

Publication date: 22 May 2023

Published in: (Search for Journal in Brave)

Abstract: We describe how the quadratic Chabauty method may be applied to explicitly determine the set of rational points on modular curves of genus $g>1$ whose Jacobians have Mordell--Weil rank $g$. This extends our previous work on the split Cartan curve of level 13 and allows us to consider modular curves that may have few known rational points or nontrivial local height contributions at primes of bad reduction. We illustrate our algorithms with a number of examples where we determine the set of rational points on several modular curves of genus 2 and 3: this includes Atkin--Lehner quotients $X_0^{+}(N)$ of prime level $N$, the curve $X_{S_4}(13)$, as well as a few other curves relevant to Mazur's Program B. We also describe the computation of rational points on the genus 6 non-split Cartan modular curve $X_{extrmns}^{+}(17)$.

Full work available at URL: https://arxiv.org/abs/2101.01862

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Quadratic Chabauty for modular curves: algorithms and examples

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6044854)