Vol. 5, No. 1, 2012

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On supersingular elliptic curves and hypergeometric functions

Keenan Monks

Vol. 5 (2012), No. 1, 99–113
Abstract

The Legendre family of elliptic curves has the remarkable property that both its periods and its supersingular locus have descriptions in terms of the hypergeometric function 2F1(12 12 1 |z). In this work we study elliptic curves and elliptic integrals with respect to the hypergeometric functions 2F1(13 23 1 |z) and 2F1(12 512 1 |z), and prove that the supersingular λ-invariant locus of certain families of elliptic curves are given by these functions.

Keywords
elliptic curves, hypergeometric functions
Mathematical Subject Classification 2010
Primary: 14H52, 33C05
Milestones
Received: 12 September 2011
Accepted: 14 September 2011
Published: 28 April 2012

Communicated by Ken Ono
Authors
Keenan Monks
Harvard University
2013 Harvard Yard Mail Center
Cambridge 02138
United States