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A class of hyperelliptic CM-curves of genus three. (English) Zbl 1066.11028
Summary: This article describes a method for constructing hyperelliptic curves of genus three whose Jacobians have complex multiplication by the maximal order in a given CM-field $$K$$. We give examples of curves defined over the rationals and over prime fields where $$K\supset\mathbb{Q}(i)$$.

##### MSC:
 11G30 Curves of arbitrary genus or genus $$\ne 1$$ over global fields 11G15 Complex multiplication and moduli of abelian varieties 14G15 Finite ground fields in algebraic geometry 14G25 Global ground fields in algebraic geometry