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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
Posted:
May 17, 1999
MathSciNet review:
1648415
Full-text PDF Free Access
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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
PII:
S 0025-5718(99)01101-1
Keywords:
CM-curves,
complex multiplication,
genus 2 curves
Received by editor(s):
December 16, 1997
Posted:
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
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