# Wydawnictwa / Czasopisma IMPAN / Acta Arithmetica / Wszystkie zeszyty

## Modular parametrizations of certain elliptic curves

### Tom 163 / 2014

Acta Arithmetica 163 (2014), 33-43 MSC: Primary 11G05; Secondary 11F11, 11F30. DOI: 10.4064/aa163-1-3

#### Streszczenie

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.

#### Autorzy

• Matija KazalickiDepartment of Mathematics
University of Zagreb
Bijenicka cesta 30
Zagreb, Croatia
e-mail
• Yuichi Sakai
• Koji TasakaGraduate School of Mathematics
Kyushu University
744 Motooka Nishiku
Fukuoka-city
Fukuoka, 819-0395, Japan
e-mail

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