Quadratic Chabauty for Atkin-Lehner quotients of modular curves via weakly holomorphic modular forms

Abstract: Quadratic Chabauty is a method to explicitly compute the rational points on certain modular curves of genus at least 2. The current algorithm, due to Balakrishnan-Dogra-Müller-Tuitman-Vonk, requires as an input an explicit plane model of the curve. The coefficients of such models grow rapidly with the genus of the curve and so are inefficient to compute with when the genus is at least 7. Therefore, we would like to replace this input with certain modular forms associated to the curve, hence creating a 'model-free' algorithm. In this talk I will provide an overview of an algorithm to compute the first stage of quadratic Chabauty on Atkin-Lehner quotients of modular curves using weakly holomorphic modular forms.

number theory

Audience: researchers in the topic

London number theory seminar

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