Are there examples of elliptic curves which has rank 0 over $\mathbb{Q}$, but acquires a high rank ( $\geq 2$) over some quadratic extension?

More generally, are there known bounds for a given extension of degree $n$, how big can the rank be if you start with a rank 0 curve ( over $\mathbb{Q}$ )?

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    $\begingroup$ The first question is easy. Take a curve $A$ over $\mathbb{Q}$ with rank as large as it can get. There exists (plenty of) quadratic twists $E$ of rank $0$. $\endgroup$ Mar 25 at 19:52

I think you will find this paper helpful: https://arxiv.org/abs/1810.04018


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