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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 ℚ, and as a consequence we generalize and explain some of their findings.
Matija Kazalicki, and Koji Tasaka. "Modular parametrizations of certain elliptic curves." Acta Arithmetica 163.1 (2014): 33-43. <http://eudml.org/doc/279785>.
@article{MatijaKazalicki2014, 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 ℚ, and as a consequence we generalize and explain some of their findings.
}, author = {Matija Kazalicki, Koji Tasaka}, journal = {Acta Arithmetica}, keywords = {modular parametrization; modular forms; Ramanujan-Serre differential operator; modular degree}, language = {eng}, number = {1}, pages = {33-43}, title = {Modular parametrizations of certain elliptic curves}, url = {http://eudml.org/doc/279785}, volume = {163}, year = {2014}, }
TY - JOUR AU - Matija Kazalicki AU - Koji Tasaka TI - Modular parametrizations of certain elliptic curves JO - Acta Arithmetica PY - 2014 VL - 163 IS - 1 SP - 33 EP - 43 AB -
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.
LA - eng KW - modular parametrization; modular forms; Ramanujan-Serre differential operator; modular degree UR - http://eudml.org/doc/279785 ER -