Integral Points on Hyperelliptic Curves

Details Integral Points on Hyperelliptic Curves Integral Points on Hyperelliptic Curves

2008-01-29

arxiv.org/abs/0801.4459v4

Algebra & Number Theory 2 (2008), No. 8, 859-885.

Mathematics

Number Theory

Scientific paper

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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