Modular curves of genus 2

Enrique González-Jiménez, Josep González

    Research output: Contribution to journalArticleResearchpeer-review

    12 Citations (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 ε S2(γ1(N)). We determine the corresponding newforms and present equations for all these curves.
    Original languageEnglish
    Pages (from-to)397-418
    JournalMathematics of Computation
    Volume71
    Issue number241
    Publication statusPublished - 1 Jan 2003

    Keywords

    • Hyperelliptic modular curves

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