Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.

Munuera Gómez, Carlos. "Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.." Extracta Mathematicae 6.2-3 (1991): 145-147. <http://eudml.org/doc/39938>.

@article{MunueraGómez1991,
abstract = {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.},
author = {Munuera Gómez, Carlos},
journal = {Extracta Mathematicae},
keywords = {Teoría algebraica de números; Curvas elípticas; Campos finitos; Números primos; Invariantes; rational points of elliptic curve defined over a finite field; deterministic algorithm},
language = {eng},
number = {2-3},
pages = {145-147},
title = {Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.},
url = {http://eudml.org/doc/39938},
volume = {6},
year = {1991},
}

TY - JOUR
AU - Munuera Gómez, Carlos
TI - Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.
JO - Extracta Mathematicae
PY - 1991
VL - 6
IS - 2-3
SP - 145
EP - 147
AB - 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.
LA - eng
KW - Teoría algebraica de números; Curvas elípticas; Campos finitos; Números primos; Invariantes; rational points of elliptic curve defined over a finite field; deterministic algorithm
UR - http://eudml.org/doc/39938
ER -