Bloch–Beilinson regulator conjecture for elliptic curves

Let $E$ be an elliptic curve over $\mathbb{Q}$, let $L(E,s)$ be its $L$-function, and let $H^2_{\mathscr{M}}(E,\mathbb{Q}(2))_{\mathbb{Z}}$ denote the integral part of its motivic cohomology. Let

r_{\mathscr{D},\mathbb{Q}\colon H^2_{\mathscr{M}}(E,\mathbb{Q}(2))\to \operatorname{Hom}(H_1(E(\mathbb{C}),\mathbb{Q})^-,\mathbb{R}(1)).

For a non-trivial $\gamma\in H_1(E(\mathbb{C}),\mathbb{Q})^-$, Bloch–Beilinson regulator conjecture. There exists $\xi\in H^2_{\mathscr{M}}(E,\mathbb{Q}(2))_{\mathbb{Z}}$ such that

$$\frac{1}{2\pi i}r_{\mathscr{D},\mathbb{Q}}(\xi)(\gamma)\equiv\frac{1}{\pi^2}L(E,2)\pmod{\mathbb{Q}^{*}}.$$

This is the explicit regulator formulation of the Bloch–Beilinson prediction for the special value $L(E,2)$; the source does not state that it has been proved in general.