Modular Curves Of Genus 2
Enrique Gonzalez-Jimenez, Josep Gonzalez
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:X1(N) --->C defined over Q and the jacobian of C, J(C), is a Q-factor of the new part of the jacobian of X1(N), J1(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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