elliptic curve; integral point; Diophantine equation
The main purpose of this paper is to prove that the elliptic curve $E\colon y^2=x^3+27x-62$ has only the integral points $(x, y)=(2, 0)$ and $(28844402, \pm 154914585540)$, using elementary number theory methods and some known results on quadratic and quartic Diophantine equations.
 Walker, D. T.: On the Diophantine equation $mx^2-ny^2=\pm 1$
. Am. Math. Mon. 74 (1967), 504-513. MR 0211954