Deines' conjecture on semi-stable non-isogenous discriminant twins

Two elliptic curves $E_1$ and $E_2$ over $\mathbb{Q}$ are discriminant twins if they have the same minimal discriminant and the same conductor. They are semi-stable if they have no additive reduction, and non-isogenous if they are not isogenous over $\mathbb{Q}$. Deines' conjecture. There are infinitely many semi-stable non-isogenous discriminant twins.