The abelian-closure conjecture for Property (N) of elliptic curves

Let $E$ be an elliptic curve defined over a number field $K$. The field $K^{\mathrm{ab}}$ is the compositum of all abelian extensions of $K$, and Property $\mathrm{(N)}$ is the property under consideration for the group of $K^{\mathrm{ab}}$-rational points. The abelian-closure conjecture. Then, $E(K^{\mathrm{ab}})$ does not have Property $\mathrm{(N)}$. This is known when $E$ has complex multiplication over $K$, because $E(K^{\mathrm{ab}})_{\mathrm{tor}}$ is then infinite; the conjecture asserts the same conclusion for every elliptic curve over every number field.