Algebra & Number Theory
- Algebra Number Theory
- Volume 2, Number 8 (2008), 859-885.
Integral points on hyperelliptic curves
Let be a hyperelliptic curve with the rational integers, , and the polynomial on the right-hand side irreducible. Let be its Jacobian. We give a completely explicit upper bound for the integral points on the model , provided we know at least one rational point on and a Mordell–Weil basis for . 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 the genus hyperelliptic models and .
Algebra Number Theory, Volume 2, Number 8 (2008), 859-885.
Received: 28 January 2008
Revised: 2 September 2008
Accepted: 12 September 2008
First available in Project Euclid: 20 December 2017
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Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir; Stoll, Michael; Tengely, Szabolcs. Integral points on hyperelliptic curves. Algebra Number Theory 2 (2008), no. 8, 859--885. doi:10.2140/ant.2008.2.859. https://projecteuclid.org/euclid.ant/1513797332