The Integral Points on Elliptic y 2 = (x − 6)(x 2 + 6x + 7)

In this paper, we studied the elliptic curve y 2 = (x – a)(x 2 + 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 y 2 = (x – 6)(x 2 + 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.