Examples of genus two CM curves defined over the rationals

  title={Examples of genus two CM curves defined over the rationals},
  author={Paul B. van Wamelen},
  journal={Math. Comput.},
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 y2 = x5−1 we find 19 non-isomorphic such curves. We believe that these are the only such curves. 
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