%0 Journal Article %T On the topological aspects of arithmetic elliptic curves %A Kazuma Morita %J Mathematics %D 2011 %I arXiv %X In this short note, we shall construct a certain topological family which contains all elliptic curves over Q and, as an application, show that this family provides some geometric interpretations of the Hasse-Weil L-function of an elliptic curve over Q whose Mordell-Weil group is of rank $\leq1$. %U http://arxiv.org/abs/1105.0850v2