Primality conjecture for elliptic Fermat numbers

Let $E$ be a fixed elliptic curve over $\mathbb{Q}$, let $P\in E(\mathbb{Q})$ be a rational point, and let $F=(F_n)_{n\in\mathbb{N}}$ be the associated sequence of elliptic Fermat numbers. Primality conjecture for elliptic Fermat numbers. The sequence $F$ contains only finitely many prime terms. This conjecture is stated for elliptic Fermat numbers associated with a fixed curve and rational point; the surrounding section indicates that the result is proved for magnified elliptic Fermat numbers, while the stated general claim is not resolved in the supplied text.