Modular Curves Of Genus 2
Number Theory
2010-06-21 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.math/0105232,
title = {Modular Curves Of Genus 2},
author = {Enrique Gonzalez-Jimenez and Josep Gonzalez},
journal= {arXiv preprint arXiv:math/0105232},
year = {2010}
}