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

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  • UserIsabel Rendell (LSGNT)
  • ClockTuesday 02 December 2025, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Dmitri Whitmore .

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.

This talk is part of the Number Theory Seminar series.

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