Let $(S,\eta,s)$ be spectrum of a discrete valuation ring $R$. Let $E$ be an elliptic curve over $\eta$. Let $\mathcal{E}$ be the Neron model of $E$.

Is there a concrete example of an $E$-torsor (smooth genus one curve over $K$) that does not extends to an $\mathcal{E}$-torsor over $S$?