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.

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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

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