  Let $C$ be a curve defined over a number field $k$. We say a closed point
$x\in C$ of degree $d$ is isolated if it does not belong to an infinite family
of degree $d$ points parametrized by the projective line or a positive rank
abelian subvariety of the curve's Jacobian. Building on work of Bourdon, Ejder,
Liu, Odumodu, and Viray, we characterize elliptic curves with rational
$j$-invariant which give rise to an isolated point of odd degree on
$X_1(N)/\mathbb{Q}$ for some positive integer $N$.
