Supersingular $p$-adic Birch and Swinnerton-Dyer conjecture

Let $E$ be an elliptic curve with good supersingular reduction at the prime $p$, let $r_E$ be its Mordell–Weil rank, and choose $\ddag\in\\{+,-\\}$. Write $f_E^{(p),\ddag}(T)=T^{r_E}g_E^{(p),\ddag}(T)$, where $g_E^{(p),\ddag}(0)$ is the remaining factor at $T=0$. Let $R_p^{\ddag}(E/\mathbb{Q})$ be the signed $p$-adic regulator, defined up to a $p$-adic unit, and write $a\sim b$ when $a/b$ is a $p$-adic unit. Supersingular $p$-adic Birch and Swinnerton-Dyer conjecture.

g_E^{(p),\ddag}(0)\sim \left(\frac{R_p^{\ddag}(E/\mathbb{Q})}{p^{r_E}}\right)\times \\#\Sha(E/\mathbb{Q})[p^{\infty}]\times \left(\prod_{l\in S^{\operatorname{bad}}}c_l(E)\right).

The source states that this is equivalent to the supersingular $p$-adic Birch and Swinnerton-Dyer conjecture and uses it conditionally in proving results for higher-rank curves.