Geodesic
Modular parametrizations of certain elliptic curves
Matija Kazalicki 1   ; Yuichi Sakai   ; Koji Tasaka 2
1 Department of Mathematics University of Zagreb Bijenicka cesta 30 Zagreb, Croatia
2 Graduate School of Mathematics Kyushu University 744 Motooka Nishiku Fukuoka-city Fukuoka, 819-0395, Japan
Acta Arithmetica, Tome 163 (2014) no. 1, pp. 33-43 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa163-1-3
Keywords: kaneko sakai recently observed certain elliptic curves whose associated newforms modularity theorem given eta quotients characterized particular differential equation involving modular forms ramanujan serre differential operator paper study certain properties modular parametrization associated elliptic curves mathbb consequence generalize explain their findings

Matija Kazalicki  1   ; Yuichi Sakai    ; Koji Tasaka  2

1 Department of Mathematics University of Zagreb Bijenicka cesta 30 Zagreb, Croatia
2 Graduate School of Mathematics Kyushu University 744 Motooka Nishiku Fukuoka-city Fukuoka, 819-0395, Japan 
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Matija Kazalicki; Yuichi Sakai; Koji Tasaka. Modular parametrizations of certain elliptic curves. Acta Arithmetica, Tome 163 (2014) no. 1, pp. 33-43. doi: 10.4064/aa163-1-3

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