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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Proving that a genus 2 curve
has complex multiplication


Author: Paul van Wamelen
Journal: Math. Comp. 68 (1999), 1663-1677
MSC (1991): Primary 14-04; Secondary 14K22
Published electronically: May 17, 1999
MathSciNet review: 1648415
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Abstract | References | Similar Articles | Additional Information

Abstract: Recently examples of genus 2 curves defined over the rationals were found which, conjecturally, should have complex multiplication. We prove this conjecture. This involves computing an explicit representation of a rational map defining complex multiplication.


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
Email: wamelen@math.lsu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01101-1
PII: S 0025-5718(99)01101-1
Keywords: CM-curves, complex multiplication, genus 2 curves
Received by editor(s): December 16, 1997
Published electronically: May 17, 1999
Additional Notes: This work was partially supported by grant LEQSF(1995-97)-RD-A-09 from the Louisiana Educational Quality Support Fund.
Article copyright: © Copyright 1999 American Mathematical Society