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

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.

legendreJNT.dvi (41828 bytes) [2001 Jun 22]
legendreJNT.dvi.gz (18603 bytes)
legendreJNT.ps.gz (66755 bytes)

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