Genus two curves with quaternionic multiplication and modular jacobian
Number Theory
2015-05-13 v1 Algebraic Geometry
Abstract
We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces with quaternionic multiplication attached to a normalized newform without complex multiplication. We include an example of with quaternionic multiplication for which we find numerically a curve whose Jacobian is up to numerical approximation, and we prove that it has quaternionic multiplication and is isogenous to .
Cite
@article{arxiv.0805.1302,
title = {Genus two curves with quaternionic multiplication and modular jacobian},
author = {Josep Gonzalez and Jordi Guardia},
journal= {arXiv preprint arXiv:0805.1302},
year = {2015}
}
Comments
15 pages, 2 figures. To appear in Mathematics of Computation