The quantitative Kurihara-number conjecture

Let $E$ be an elliptic curve over $\mathbb{Q}$ of conductor $N$, let $p\geq5$ be a prime, and let $\widetilde{\boldsymbol{\delta}}$ be the collection of Kurihara numbers. Assume that $\overline{\rho}$ is surjective and that the Manin constant is prime to $p$. Quantitative Kurihara-number conjecture. Then

$$\partial^{(\infty)}(\widetilde{\boldsymbol{\delta}})=\sum_{\ell\mid N}\operatorname{ord}_p(c_\ell),$$

where $c_\ell$ is the Tamagawa factor of $E$ at $\ell$. This is described as a quantitative refinement of the non-vanishing conjecture and as compatible with the classical Birch--Swinnerton-Dyer formula; the supplied text does not resolve it.