Modular curves of genus 2

Enrique González-Jiménez; Josep González

doi:10.1090/S0025-5718-02-01458-8

Modular curves of genus 2

Enrique González-Jiménez, Josep González

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

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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 ∊ S2(Γ1(N)). We determine the corresponding newforms and present equations for all these curves. © 2002 American Mathematical Society.

Original language	English
Pages (from-to)	397-418
Journal	Mathematics of Computation
Volume	72
Issue number	241
DOIs	https://doi.org/10.1090/S0025-5718-02-01458-8
Publication status	Published - 1 Jan 2002

Keywords

Hyperelliptic modular curves

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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 ∊ S2(Γ1(N)). We determine the corresponding newforms and present equations for all these curves. {\textcopyright} 2002 American Mathematical Society.",

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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 ∊ S2(Γ1(N)). We determine the corresponding newforms and present equations for all these curves. © 2002 American Mathematical Society.

KW - Hyperelliptic modular curves

U2 - 10.1090/S0025-5718-02-01458-8

DO - 10.1090/S0025-5718-02-01458-8

M3 - Article

VL - 72

SP - 397

EP - 418

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 241

ER -