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Legendre elliptic curves over finite fields

Roland Auer·Jaap Top
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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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Roland Auer, Jaap Top. 2001-06-22. Legendre elliptic curves over finite fields. https://arxiv.org/abs/math/0106273

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