Is there a specific method to solve equations like $ y^2 = x^3 - n^2x $ ? I was reading an example about $ y^2 = x^3 - 49x $ and it says that a solution is $ (-\frac{63}{16},\frac{735}{64}) $ . How did he find it? Thanks
In some papers I saw that if I find a solution $ (x_{0},y_{0}) $ and replace $ x $ with $ x-x_{0} $ and $ y $ with $ y=kx+y_{0} $ I will find all rational solutions.