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arXiv · 1604.07774

Eta quotients, Eisenstein series and Elliptic Curves

Ayse Alaca·Saban Alaca·Zafer Selcuk Aygin
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Abstract

We express all the newforms of weight $2$ and levels $30$, $33$, $35$, $38$, $40$, $42$, $44$, $45$ as linear combinations of eta quotients and Eisenstein series, and list their corresponding strong Weil curves. Let $p$ denote a prime and $E (\zz_p)$ denote the the group of algebraic points of an elliptic curve $E$ over $\zz_p$. We give a generating function for the order of $E (\zz_p)$ for certain strong Weil curves in terms of eta quotients and Eisenstein series. We then use our generating functions to deduce congruence relations for the order of $E (\zz_p)$ for those strong Weil curves.

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Ayse Alaca, Saban Alaca, Zafer Selcuk Aygin. 2016-04-26. Eta quotients, Eisenstein series and Elliptic Curves. https://arxiv.org/abs/1604.07774

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