Integral points on hyperelliptic curves

Yann Bugeaud, Maurice Mignotte, Samir Siksek, Michael Stoll, Szabolcs Tengely
2008 Algebra & Number Theory  
Let C : Y 2 = a n X n + · · · + a 0 be a hyperelliptic curve with the a i rational integers, n ≥ 5, and the polynomial on the right-hand side irreducible. Let J be its Jacobian. We give a completely explicit upper bound for the integral points on the model C, provided we know at least one rational point on C and a Mordell-Weil basis for J ‫.)ޑ(‬ We also explain a powerful refinement of the Mordell-Weil sieve which, combined with the upper bound, is capable of determining all the integral
more » ... Our method is illustrated by determining the integral points on the genus 2 hyperelliptic models Y 2 − Y = X 5 − X and Y 2 = X 5 . MSC2000: primary 11G30; secondary 11J86.
doi:10.2140/ant.2008.2.859 fatcat:a3iii577cnbu7f7bd74b2vu6du