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$\mathbb{Q}$
Extending the idea of Dabrowski [‘On the proportion of rank 0 twists of elliptic curves’, C. R. Acad. Sci. Paris, Ser. I 346 (2008), 483–486] and using the 2-descent method, we provide three general families of elliptic curves over 
$\mathbb{Q}$ such that a positive proportion of prime-twists of such elliptic curves have rank zero simultaneously.
