Plane quartics over $\mathbb {Q}$ with complex multiplication
Pınar Kılıçer, Hugo Labrande, Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling, Marco Streng · Acta Arithmetica · 2018
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