Legendre elliptic curves over finite fields

2001/06/22 by Roland Auer, Auer, Roland, Jaap Top +1 · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0106273

arxiv created 2001/06/22 · arxiv updated 2009/12/01

Abstract

We show that every elliptic curve over a finite field of odd characteristic whose number of rational points is divisible by 4 is isogenous to an elliptic curve in Legendre form, with the sole exception of a minimal respectively maximal elliptic curve. We also collect some results concerning the supersingular Legendre parameters.

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