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arXiv · 1202.0337

Elliptic Curves, eta-quotients, and hypergeometric functions

Eugene Yoong·David Pathakjee·Zef Rosnbrick
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Abstract

The well-known fact that all elliptic curves are modular, proven by Wiles, Taylor, Breuil, Conrad and Diamond, leaves open the question whether there exists a 'nice' representation of the modular form associated to each elliptic curve. Here we provide explicit representations of the modular forms associated to certain Legendre form elliptic curves 2_E_1(λ) as linear combinations of quotients of Dedekind's eta-function. We also give congruences for some of the modular forms' coefficients in terms of Gaussian hypergeometric functions.

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Eugene Yoong, David Pathakjee, Zef Rosnbrick. 2012-02-02. Elliptic Curves, eta-quotients, and hypergeometric functions. https://arxiv.org/abs/1202.0337

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