The Mathematical Institute, University of Oxford, Eprints Archive

Descent via isogeny in dimension 2

Flynn, E. V. (1994) Descent via isogeny in dimension 2. Acta Arithmetica, LXVI (1). pp. 23-43. ISSN 0065-1036

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Abstract

A technique of descent via 4-isogeny is developed on the Jacobian of a curve of genus 2 of the form: $Y^2 = q_1(X)q_2(X)q_3(X)$, where each $q_i(X)$ is a quadratic defined over Q. The technique offers a realistic prospect of calculating rank tables of Mordell-Weil groups in higher dimension. A selection of worked examples is included as illustration.

Item Type:Article
Uncontrolled Keywords:Descent via isogeny; ranks; Mordell-Weil group.
Subjects:A - C > Algebraic geometry
H - N > Number theory
Research Groups:Number Theory Group
ID Code:270
Deposited By:E. Victor Flynn
Deposited On:12 Jul 2006
Last Modified:20 Jul 2009 14:19

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