  We give parametrisation of curves C of genus 2 with a maximal isotropic
(ZZ/3)^2 in J[3], where J is the Jacobian variety of C, and develop the theory
required to perform descent via (3,3)-isogeny. We apply this to several
examples, where it can shown that non-reducible Jacobians have nontrivial
3-part of the Tate-Shafarevich group.
