Integral points on hyperelliptic curves
Copyright policy )Integral points on hyperelliptic curves
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.
- Hungarian Academy of Sciences Hungary
- University of Warwick United Kingdom
- University of Debrecen Hungary
- University of Bayreuth Germany
- UNIVERSITE MARIE ET LOUIS PASTEUR France
11G30, Mathematics - Number Theory, integral point, 11J86, Mordell–Weil sieve, 11G30, 11J86, Baker's bound, FOS: Mathematics, Number Theory (math.NT), curve, Jacobian, Mordell–Weil group, height
11G30, Mathematics - Number Theory, integral point, 11J86, Mordell–Weil sieve, 11G30, 11J86, Baker's bound, FOS: Mathematics, Number Theory (math.NT), curve, Jacobian, Mordell–Weil group, height
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