Modular curves of genus 2

Enrique González-Jiménez, Josep González

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    1 Citation (Scopus)

    Abstract

    We prove that there are exactly 149 genus two curves C defined over ℚ such that there exists a nonconstant morphism π: X1(N) → C defined over ℚ and the jacobian of C is ℚ -isogenous to the abelian variety Af attached by Shimura to a newform f ∊ S2(Γ1(N)). We determine the corresponding newforms and present equations for all these curves. © 2002 American Mathematical Society.
    Original languageEnglish
    Pages (from-to)397-418
    JournalMathematics of Computation
    Volume72
    Issue number241
    DOIs
    Publication statusPublished - 1 Jan 2002

    Keywords

    • Hyperelliptic modular curves

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