# Plane quartics over Q with complex multiplication

3 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2017-13. 34 pages. 2017
Domaine :

https://hal.archives-ouvertes.fr/hal-01455036
Contributeur : Marie-Annick Guillemer <>
Soumis le : vendredi 3 février 2017 - 11:10:10
Dernière modification le : mardi 17 avril 2018 - 09:05:35

### Identifiants

• HAL Id : hal-01455036, version 1
• ARXIV : 1701.06489

### Citation

Pinar Kilicer, Hugo Labrande, Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling, et al.. Plane quartics over Q with complex multiplication. 2017-13. 34 pages. 2017. 〈hal-01455036〉

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