Modular curves of genus 2

Enrique González-Jiménez; Josep González

Modular curves of genus 2

Enrique González-Jiménez, Josep González

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

14 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 language	English
Pages (from-to)	397-418
Journal	Mathematics of Computation
Volume	71
Issue number	241
Publication status	Published - 1 Jan 2003

Keywords

Hyperelliptic modular curves

Cite this

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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.",

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AB - 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.

KW - Hyperelliptic modular curves

M3 - Article

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VL - 71

SP - 397

EP - 418

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 241

ER -

Modular curves of genus 2

Abstract

Keywords

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