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

Título inglés	Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.
Título español	Curvas elípticas con j-invariante igual a 0 ó 1728 sobre un campo primo finito.
Autor/es	Munuera Gómez, Carlos
Organización	Dep. Mat. Apl. Fund. Esc. Téc. Sup. Arquit. Univ. Valladolid, Valladolid, España
Revista	0213-8743
Publicación	1991, 6 (2-3): 145-147, 3 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	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 Î 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.
Clasificación UNESCO	120501 ; 120101
Palabras clave español	Teoría algebraica de números ; Curvas elípticas ; Campos finitos ; Números primos ; Invariantes
Código MathReviews	MR1185363
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