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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 familyof degree $d$ points parametrized by the projective line or a positive rankabelian 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 $N$.

Odd degree isolated points on $X_1(N)$ with rational $j$-invariant