Examples of genus two CM curves defined over the rationals |
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Authors: | Paul van Wamelen. |
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Affiliation: | Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918 |
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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 we find 19 non-isomorphic such curves. We believe that these are the only such curves. |
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