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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
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