Finiteness of local torsion primes for non-CM elliptic curves

Let $E$ be an elliptic curve over ${\mathbf Q}$, and let $d\geq 1$ be fixed. A prime $p$ is a local torsion prime for $E$ if there exists an extension $K/{\mathbf Q}_p$ of degree at most $d$ such that $E(K)[p]\neq 0$. Finiteness conjecture. If $E$ does not have complex multiplication, then there are only finitely many such primes $p$. This conjecture predicts that non-CM elliptic curves have finitely many local torsion primes of uniformly bounded local degree; the paper presents it as motivated by simple heuristics and numerical data, with no resolution supplied here.