Plane quartics over Q with complex multiplication

arXiv: Number Theory, 2016.

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Abstract:

We give examples of smooth plane quartics over $Q$ with complex multiplication over $overline{Q}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of period matrices, the fast computation of Dixmier-Ohno invariants, and reconstruction from these invariants. Finally, we di...More

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