Range of rank in an elliptic curve (Q2844393)

Let \(p\) be a prime number congruent to \(13,15\) modulo \(16\). The authors show that the rank of \(\mathbb{Q}\)-rational points group of the elliptic curve \(y^2=x^3+px\) is \(0\) or \(1\). For a more precise result, refer to proposition 6.2 of chapter X of \textit{J. H. Silverman} [The arithmetic of elliptic curves. 2nd ed. Graduate Texts in Mathematics 106. New York, NY: Springer (2009; Zbl 1194.11005)].