Legendre elliptic curves over finite fields, by Roland Auer and Jaap Top

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.

Roland Auer and Jaap Top <auer@math.rug.nl,top@math.rug.nl>