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

    Acta Arithmetica, pp. 127-156, 2018.

    Cited by: 2|Bibtex|Views0|
    Keywords:
    complex multiplicationgenus 3plane quarticsexplicit aspects

    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, ...More

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