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.
Original language | English |
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Pages (from-to) | 127-156 |
Number of pages | 25 |
Journal | Acta Arithmetica |
Volume | 185 |
Issue number | 2 |
DOIs | |
Publication status | Published - 13-Jul-2018 |
Keywords
- math.NT
- math.AG