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2012 On supersingular elliptic curves and hypergeometric functions
Keenan Monks
Involve 5(1): 99-113 (2012). DOI: 10.2140/involve.2012.5.99

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(12121|z). In this work we study elliptic curves and elliptic integrals with respect to the hypergeometric functions 2F1(13231|z) and 2F1(125121|z), and prove that the supersingular λ-invariant locus of certain families of elliptic curves are given by these functions.

Citation

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Keenan Monks. "On supersingular elliptic curves and hypergeometric functions." Involve 5 (1) 99 - 113, 2012. https://doi.org/10.2140/involve.2012.5.99

Information

Received: 12 September 2011; Accepted: 14 September 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1247.14039
MathSciNet: MR2924318
Digital Object Identifier: 10.2140/involve.2012.5.99

Subjects:
Primary: 14H52, 33C05

Rights: Copyright © 2012 Mathematical Sciences Publishers

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