Representation of integers by positive ternary quadratic forms

Let m be a positive integer satisfying m equivalent to 1 (mod 4) and (m/7) = 1. Then there exist integers x, y, epsilon Z such that m = x(2) + 7y(2) + 49z(2). Recent work of J. Coates, Y. Li, Y. Tian and S. Zhai ([1]) shows that this conclusion is useful in the study of the arithmetic of elliptic curves. The above m can be represented also by either x2 + 14y2 + 28z2 + 14yz or 2x(2) + 4y(2) + 49z(2) + 2xy. Moreover, if m = 1 (mod 8) and (m/7) = 1, then m can be represented by x(2) + 14y(2) + 28z(2) + 14yz. The same is true for 2x(2) + 4y(2) + 49z(2) + 2xy, provided that m is not square. If we assume further that m = 1 (mod 4) with (m/7) = 1 is not square, then m can be represented by 8x(2) + 8y(2) + 9z(2) + 8yz + 8xz + 2xy and 2x(2) + 7y(2) + 25z(2) + 2xz. Note that the genus of x(2) + 7y(2) + 49z(2) consists of exactly the above appeared five ternary quadratic forms.