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Mathematics of Computation

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Examples of genus two CM curves
defined over the rationals

Author: Paul van Wamelen
Journal: Math. Comp. 68 (1999), 307-320
MSC (1991): Primary 14-04; Secondary 14K22
MathSciNet review: 1609658
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Abstract: We present the results of a systematic numerical search for genus two curves defined over the rationals such that their Jacobians are simple and have endomorphism ring equal to the ring of integers of a quartic CM field. Including the well-known example $y^2 = x^5 - 1$ we find 19 non-isomorphic such curves. We believe that these are the only such curves.

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Additional Information

Paul van Wamelen
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918

Received by editor(s): June 13, 1996
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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