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

Abstract : We give examples of smooth plane quartics over QQQ with complex multiplication over Q¯¯¯¯Q¯\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.
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https://hal.archives-ouvertes.fr/hal-01856433
Contributor : Christophe Ritzenthaler <>
Submitted on : Saturday, August 11, 2018 - 11:10:49 AM
Last modification on : Monday, March 4, 2019 - 2:04:22 PM

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Pınar Kılıçer, Hugo Labrande, Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling, et al.. Plane quartics over $\mathbb {Q}$ with complex multiplication. Acta Arithmetica, Instytut Matematyczny PAN, 2018, ⟨10.4064/aa170227-16-3⟩. ⟨hal-01856433⟩

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