Modular Curves of genus 2, by Enrique González-Jiménez and Josep González

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.

Enrique González-Jiménez and Josep González <enrikegj@mat.uab.es, josepg@mat.upc.es>