Examples of genus two CM curves defined over the rationals
Open Access
- 1 January 1999
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 68 (225) , 307-320
- https://doi.org/10.1090/s0025-5718-99-01020-0
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 we find 19 non-isomorphic such curves. We believe that these are the only such curves.Keywords
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