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

Extracta Mathematicae (1991)

- Volume: 6, Issue: 2-3, page 145-147
- ISSN: 0213-8743

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topMunuera 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 -

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