## Involve: A Journal of Mathematics

• Involve
• Volume 5, Number 1 (2012), 1-8.

### Elliptic curves, eta-quotients and hypergeometric functions

#### 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 $2E1(λ)$ 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.

#### Article information

Source
Involve, Volume 5, Number 1 (2012), 1-8.

Dates
Revised: 22 April 2011
Accepted: 14 September 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.involve/1513733443

Digital Object Identifier
doi:10.2140/involve.2012.5.1

Mathematical Reviews number (MathSciNet)
MR2924308

Zentralblatt MATH identifier
1284.11072

#### Citation

Pathakjee, David; RosnBrick, Zef; Yoong, Eugene. Elliptic curves, eta-quotients and hypergeometric functions. Involve 5 (2012), no. 1, 1--8. doi:10.2140/involve.2012.5.1. https://projecteuclid.org/euclid.involve/1513733443

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