Pinar Kilicer, Hugo Labrande, Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling, Marco Streng
Published 2017-01-23Version 1
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 discuss some of the reduction properties of the curves that we obtain.
The theory of complex multiplication for K3 surfaces
Bad reduction of genus $3$ curves with complex multiplication
The fundamental theorem of complex multiplication
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