### 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>