We give a new and efficient method of sieving for rational points#R##N#on hyperelliptic curves. This method is often successful in proving that a#R##N#given hyperelliptic curve, suspected to have no rational points, does in fact#R##N#have no rational points; we have often found this to be the case even when our#R##N#curve has points over all localizations Qp. We illustrate the practicality of the#R##N#method with some examples of hyperelliptic curves of genus 1.
['Samir Siksek']
Sieving for rational points on hyperelliptic curves