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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
Posted:
August 18, 1999
MathSciNet review:
1677415
Full-text PDF Free Access
Abstract |
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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.
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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
Email:
wamelen@math.lsu.edu
DOI:
http://dx.doi.org/10.1090/S0025-5718-99-01179-5
PII:
S 0025-5718(99)01179-5
Keywords:
Isogenies,
genus 2 curves,
good reduction
Received by editor(s):
June 9, 1998
Received by editor(s) in revised form:
December 7, 1998
Posted:
August 18, 1999
Article copyright:
© Copyright 2000 American Mathematical Society
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