# zbMATH — the first resource for mathematics

Rational points on elliptic curves. (English. Russian original) Zbl 0742.14016
Proc. Steklov Inst. Math. 183, 19-26 (1991); translation from Tr. Mat. Inst. Steklova 183, 22-29 (1990).
For a non-zero integer $$A$$ consider the elliptic curve given by the equation $$x^ 3+y^ 3=Az^ 3$$. This curve was studied by D. K. Fadeev in 1934 who gave estimates of its rank and found informations about the group of its rational points. The aim of the present paper is to take up the study of the arithmetic of this curve from a modern point of view. In particular, the author proves that Mazur’s conjecture for this curve holds true.
##### MSC:
 14G05 Rational points 14H52 Elliptic curves
##### Keywords:
elliptic curve; rational points