The integral points on elliptic curves y2 = x3+(36n2- 9)x-2(36n2-5)

Let n be a positive odd integer. In this paper, combining some properties of quadratic and quartic diophantine equations with elementary analysis, we prove that if n > 1 and both 6n(2) - 1 and 12n(2) + 1 are odd primes, then the general elliptic curve y(2) = x(3)+(36n(2)-9)x-2(36n(2)-5) has only the integral point (x, y) = (2, 0). By this result we can get that the above elliptic curve has only the trivial integral point for n = 3, 13, 17 etc. Thus it can be seen that the elliptic curve y(2) = x(3) + 27x-62 really is an unusual elliptic curve which has large integral points.