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Construction of CM Picard curves. (English) Zbl 1049.14014
Summary: We generalize the CM method for elliptic and hyperelliptic curves to Picard curves. We describe the algorithm in detail and discuss the results of our implementation.

MSC:
14G50 Applications to coding theory and cryptography of arithmetic geometry
14H45 Special algebraic curves and curves of low genus
11G15 Complex multiplication and moduli of abelian varieties
14K22 Complex multiplication and abelian varieties
Software:
ECPP; PARI/GP
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