Canonical heights on the jacobians of curves of genus 2 and the infinite descent

We give an algorithm to compute the canonical height on a Jacobian of a curve of genus 2. The computations involve only working with the Kummer surface and so lengthy computations with divisors in the Jacobian are avoided. We use this height algorithm to give an algorithm to perform the infinite descent stage of computing the Mordell-Weil group. This last stage is performed by a lattice enlarging procedure.

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