finding rational points on an elliptic curve
Consider the following elliptic curve
It is trivial that the points $P_1(-1540,0)$, $P_2(508,0)$ and $P_3(65024,0)$ lie on this curve. It is also quite easy to find four other integer points $P_4(-508, 262128)$, $P_5(-508, -262128)$, $P_6(130556, 33552384)$ and $P_7(130556, -33552384)$.
I want to find some other rational points on this curve. If one uses the usual group law we obtain that for every $1\le i \le j \le 7$ we have $P_i+P_j=P_k$ for some $1\le k\le 7$. Thus we fail to obtain any new points.
Any suggestion would be appreciated.