Let p be a prime number, p ≠ 2,3 and Fp the finite field with p elements. An elliptic curve E over Fp is a projective nonsingular curve of genus 1 defined over Fp. Each one of these curves has an isomorphic model given by an (Weierstrass) equation E: y2 = x3 + Ax + B, A,B ∈ Fp with D = 4A3 + 27B2 ≠ 0. The j-invariant of E is defined by j(E) = 1728·4A3/D.
The aim of this note is to establish some results concerning the cardinality of the group of points on elliptic curves over Fp with j-invariants equals to 0 or 1728, and the connection between these cardinalities and some expressions of sum of squares.
@article{urn:eudml:doc:39938,
title = {Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.},
journal = {Extracta Mathematicae},
volume = {6},
year = {1991},
pages = {145-147},
mrnumber = {MR1185363},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39938}
}
Munuera Gómez, Carlos. Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.. Extracta Mathematicae, Tome 6 (1991) pp. 145-147. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39938/