Injectivity of the specialization homomorphism of elliptic curves

Ivica Gusić, Petra Tadić

Let $E:y^2=x^3+A{x}^2+Bx+C$ be a nonconstant elliptic curve over $\mathbb{Q}(t)$ with at least one nontrivial $\mathbb{Q}(t)$-rational $2$-torsion point. We describe a method for fin…