David–Weston conjecture on local torsion primes

Let $E/\mathbb{Q}$ be an elliptic curve without complex multiplication. A prime $p$ is a local torsion prime when $E$ has good reduction at $p$ and $E(\mathbb{Q}_p)[p]\neq 0$. David–Weston conjecture. The set of local torsion primes of $E$ is finite. The source says that this conjecture is supported by heuristics based on the distribution of Frobenius traces and $p$-adic lifts, but gives no resolution.