%0 Journal Article
%T Generalized Legendre curves and Quaternionic Multiplication
%A Alyson Deines
%A Jenny G. Fuselier
%A Ling Long
%A Holly Swisher
%A Fang-Ting Tu
%J Mathematics
%D 2014
%I arXiv
%R 10.1016/j.jnt.2015.04.019
%X This paper is devoted to abelian varieties arising from generalized Legendre curves. In particular, we consider their corresponding Galois representations, periods, and endomorphism algebras. For certain one parameter families of 2-dimensional abelian varieties of this kind, we determine when the endomorphism algebra of each fiber defined over the algebraic closure of $\Bbb Q$ contains a quaternion algebra.
%U http://arxiv.org/abs/1412.6906v3