The positive integral points on the elliptic curve y2 = (x + 4)(x2 − 4x + 5)

Abstract

In this paper, we studied the elliptic curve y2 = (x – a)(x2 + ax + r), a, r ∈ Z+ in the case of a = 6,r = 7 which has no relevant conclusions up to now. And we obtained the conclusion of the integer points on Elliptic y2 = (x – 6)(x2 + 6x + 7), elliptic curve in title has only one integer point (x, y) = (6,0) were proved with the help of the elementary methods such as congruence and Legendre symbol.