Modular parametrizations of certain elliptic curves
Volume 163 / 2014
Acta Arithmetica 163 (2014), 33-43
MSC: Primary 11G05; Secondary 11F11, 11F30.
DOI: 10.4064/aa163-1-3
Abstract
Kaneko and Sakai (2013) 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 the modular parametrization associated to the elliptic curves over $\mathbb {Q}$, and as a consequence we generalize and explain some of their findings.
