Rational Points on Elliptic K3 Surfaces of Quadratic Twist Type
Rational Points on Elliptic K3 Surfaces of Quadratic Twist Type
In studying rational points on elliptic K3 surfaces of the form $f(t)y^2=g(x)$, where $f,g$ are cubic or quartic polynomials (without repeated roots), we introduce a condition on the quadratic twists of two elliptic curves having simultaneously positive Mordell-Weil rank. We prove a necessary and sufficient condition for the Zariski density …