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SUMMARY:Quadratic Chabauty for Atkin-Lehner quotients of modular curves vi
 a weakly holomorphic modular forms. - Isabel Rendell (LSGNT)
DTSTART:20251202T143000Z
DTEND:20251202T153000Z
UID:TALK238003@talks.cam.ac.uk
CONTACT:Dmitri Whitmore
DESCRIPTION:Quadratic Chabauty is a method to explicitly compute the ratio
 nal points on certain modular curves of genus at least 2. The current algo
 rithm\, due to Balakrishnan-Dogra-Müller-Tuitman-Vonk\, requires as an in
 put 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 t
 his input with certain modular forms associated to the curve\, hence creat
 ing a 'model-free' algorithm. In this talk I will provide an overview of a
 n algorithm to compute the first stage of quadratic Chabauty on Atkin-Lehn
 er quotients of modular curves using weakly holomorphic modular forms.
LOCATION:MR13
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