Determining explicitly the Mordell-Weil group of certain rational elliptic surfaces

Remke Kloosterman

Let $A,B$ be nonzero rational numbers. Consider the elliptic curve $E_{A,B}/\mathbb{Q}(t)$ with Weierstrass equation $y^2=x^3+A{t}^6+B$. An algorithm to determine $\mathrm{rank } E_{…