A CM construction for curves of genus 2 with p-rank 1

    Journal of Number Theory, 2011.

    Cited by: 12|Bibtex|Views4|Links
    EI
    Keywords:
    finite fieldcomplex multiplicationalgebraic geometry

    Abstract:

    We construct Weil numbers corresponding to genus-2 curves with $p$-rank 1 over the finite field $\F_{p^2}$ of $p^2$ elements. The corresponding curves can be constructed using explicit CM constructions. In one of our algorithms, the group of $\F_{p^2}$-valued points of the Jacobian has prime order, while another allows for a prescribed ...More

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