Plane quartics over Q with complex multiplication

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

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9 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)127-156
Number of pages25
JournalActa Arithmetica
Issue number2
Publication statusPublished - 13-Jul-2018


  • math.NT
  • math.AG

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