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 ℚ, and as a consequence we generalize and explain some of their findings.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-1-3,
author = {Matija Kazalicki and Koji Tasaka},
title = {Modular parametrizations of certain elliptic curves},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {33-43},
zbl = {1300.11062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-1-3}
}
Matija Kazalicki; Koji Tasaka. Modular parametrizations of certain elliptic curves. Acta Arithmetica, Tome 166 (2014) pp. 33-43. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-1-3/