On a theorem of Coleman

A simplified method of descent via isogeny is given for Jacobians of curves of genus 2. This method is then used to give applications of a theorem of Coleman for computing all of the rational points on certain curves of genus 2

A flexible method for applying Chabauty's Theorem

A strategy is proposed for applying Chabauty's Theorem to hyperelliptic curves of genus>1. In the genus 2 case, it shown how recent developments on the formal group of the Jacobian can be used to give a flexible and computationally viable method for applying this strategy. The details are described for a general curve of genus 2, and are then applied to find C(Q) for a selection of curves. A fringe benefit is a more explicit proof of a result of Coleman