I am following book "Rational Points on Elliptic Curves" by Silverman-Tate(basic version not the "The Arithmetic of Elliptic Curves" by Silverman-Tate) And I am trying to solve for cubic curve, $y^2=x^3+px$ where $p$ is prime
1) Rank of the curve is $0,1$ or$ 2$.
Using the standard methods described in that book. I am considering various equations of the form $N^2 = b1M^4+b2e^4$ where $b_1.b_2=b$ to check if there is any solutions modulo $p$ and considering quadratic residue modulo $p$.
I know that this same questions were asked previously but currently I am not familiar with the content of "The Arithmetic of Elliptic Curves" by Silverman-Tate)". So I need to prove what is currently in "Rational Points on Elliptic Curves" (by Silverman-Tate).
Any kind of help is much appreciated.