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Modular Curves Of Genus 2

Enrique Gonzalez-Jimenez·Josep Gonzalez
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Abstract

We prove that there is only a finite number of genus 2 curves C defined over Q such that there exists a nonconstant morphism pi:X_1(N) --->C defined over Q and the jacobian of C, J(C), is a Q-factor of the new part of the jacobian of X_1(N), J_1(N)^{new}. Moreover, we prove that there are only 149 genus two curves of this kind with the additional requeriment that their jacobians are Q-simple. We determine the corresponding newforms and present equations for all these curves.

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Enrique Gonzalez-Jimenez, Josep Gonzalez. 2001-05-28. Modular Curves Of Genus 2. https://doi.org/10.1090/s0025-5718-02-01458-8

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