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arXiv · 1701.06489

Plane quartics over $\mathbb{Q}$ with complex multiplication

Pınar Kılıçer·Hugo Labrande·Reynald Lercier·Christophe Ritzenthaler·Jeroen Sijsling·Marco Streng
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Abstract

We give examples of smooth plane quartics over $\mathbb{Q}$ with complex multiplication over $\overline{\mathbb{Q}}$ 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.

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Pınar Kılıçer, Hugo Labrande, Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling, Marco Streng. 2022-04-08. Plane quartics over $\mathbb{Q}$ with complex multiplication. https://doi.org/10.4064/aa170227-16-3

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