how to calculate rank of elliptic curve

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I study about elliptic curve and I saw Rank of the elliptic curve $y^2=x^3+px$ but i can't understand how he can calculate $$2M^4−2pe^4=N^2$$ $$4M^4−pe^4=N^2$$

how he revived to this formulas? what mean of $e, M, N$?