Density-zero conjecture for p-divisible p-adic regulators

Let $E$ be an elliptic curve over $\mathbb{Q}$ and let $K$ be a number field. For each prime $p$, let $R_p(E/K)$ denote the $p$-adic regulator. Density-zero regulator conjecture. The set of primes $p$ such that $R_p(E/K)$ is divisible by $p$ has density zero. This conjecture predicts that divisibility of the $p$-adic regulator by the corresponding prime is exceptional; the paper presents it as an extrapolation from computations over $\mathbb{Q}$ to general number fields.