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Mathematics of Computation

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Poonen's question concerning isogenies
between Smart's genus 2 curves

Author: Paul van Wamelen
Journal: Math. Comp. 69 (2000), 1685-1697
MSC (1991): Primary 14-04; Secondary 14K02
Published electronically: August 18, 1999
MathSciNet review: 1677415
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Abstract | References | Similar Articles | Additional Information

Abstract: We describe a method for proving that two explicitly given genus two curves have isogenous jacobians. We apply the method to the list of genus 2 curves with good reduction away from 2 given by Smart. This answers a question of Poonen.

References [Enhancements On Off] (What's this?)

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Additional Information

Paul van Wamelen
Affiliation: Department of Mathematics, University of South Africa, P. O. Box 392, Pretoria, 0003, South Africa
Address at time of publication: Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918

Keywords: Isogenies, genus 2 curves, good reduction
Received by editor(s): June 9, 1998
Received by editor(s) in revised form: December 7, 1998
Published electronically: August 18, 1999
Article copyright: © Copyright 2000 American Mathematical Society