The Mathematical Institute, University of Oxford, Eprints Archive

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

Flynn, E. V. and Smart, N. P. (1997) Canonical heights on the jacobians of curves of genus 2 and the infinite descent. Acta Arithmetica, LXXIX (4). pp. 333-352. ISSN 0065-1036

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Canonical height; Jacobian; Kummer surface.
Subjects:A - C > Algebraic geometry
H - N > Number theory
Research Groups:Number Theory Group
ID Code:264
Deposited By:E. Victor Flynn
Deposited On:12 Jul 2006
Last Modified:20 Jul 2009 14:19

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