# Plane quartics over Q with complex multiplication

Pinar Kilicer, Hugo Labrande, Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling, Marco Streng

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6 Citaten (Scopus)
216 Downloads (Pure)

## Samenvatting

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.
Originele taal-2 English 127-156 25 Acta Arithmetica 185 2 https://doi.org/10.4064/aa170227-16-3 Published - 13-jul-2018