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arXiv · 0801.4459

Integral Points on Hyperelliptic Curves

Y. Bugeaud·M. Mignotte·S. Siksek·M. Stoll·Sz. Tengely
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Abstract

We give a completely explicit upper bound for integral points on (standard) affine models of hyperelliptic curves, provided we know at least one rational point and a Mordell-Weil basis of the Jacobian. We also explain a powerful refinement of the Mordell--Weil sieve which, combined with the upper bound, is capable of determining all the integral points. Our method is illustrated by determining the integral points on a two genus 2 hyperelliptic curves with Mordell--Weil Jacobian ranks of 3 and 6.

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Y. Bugeaud, M. Mignotte, S. Siksek, M. Stoll, Sz. Tengely. 2010-03-16. Integral Points on Hyperelliptic Curves. https://arxiv.org/abs/0801.4459

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