Quadratic Chabauty for modular curves: algorithms and examples

Netan Dogra, Jennifer Balakrishnan, Jan Steffen Müller, Jan Tuitman, Jan Vonk

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We describe how the quadratic Chabauty method may be applied to determine the set of rational points on modular curves of genus 1]]> whose Jacobians have Mordell-Weil rank. 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 non-trivial 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 of prime level, the curve, as well as a few other curves relevant to Mazur's Program B. We also compute the set of rational points on the genus 6 non-split Cartan modular curve.

Original languageEnglish
Article number159
Pages (from-to) 1111 - 1152
Number of pages42
JournalCOMPOSITIO MATHEMATICA
Volume159
Issue number6
DOIs
Publication statusPublished - 15 May 2023

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