  We present a heuristic asymptotic formula as $x\to \infty$ for the number of
isogeny classes of pairing-friendly elliptic curves with fixed embedding degree
$k\geq 3$, with fixed discriminant, with rho-value bounded by a fixed $\rho_0$
such that $1<\rho_0<2$, and with prime subgroup order at most $x$.
