  Kaneko and Sakai recently observed that certain elliptic curves whose
associated newforms (by the modularity theorem) are given by the eta-quotients
can be characterized by a particular differential equation involving modular
forms and Ramanujan-Serre differential operator. In this paper, we study
certain properties of modular parametrizations associated to the elliptic
curves over Q, and as a consequence we generalize and explain some of their
findings.
