Isolated points on X-1(l(n)) with rational j-invariant

Let l be a prime and let n >= 1. In this note we show that if there is a non-cuspidal, non-CM isolated point x with a rational j-invariant on the modular curve X-1(l(n)), then l = 37 and the j-invariant of x is either 7 center dot 11(3) or -7.137(3) center dot 2083(3). The reverse implication holds for the first j-invariant but it is currently unknown whether or not it holds for the second.