Integral points on the congruent number curve

Published: Apr 29, 2022
Abstract
We study integral points on the quadratic twists \mathcal{E}_D:y^2=x^3-D^2xof the congruent number curve. We give upper bounds on the number of integral points in each coset of 2\mathcal{E}_D(\mathbb{Q})in \mathcal{E}_D(\mathbb{Q})and show that their total is \ll (3.8)^{\mathrm{rank} \mathcal{E}_D(\mathbb{Q})} We further show that the average number of non-torsion integral points in this family is bounded above by 2 As an...
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Title
Integral points on the congruent number curve
Published Date
Apr 29, 2022
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