We construct three p-adic L-functions attached to the symmetric square of a modular elliptic curve. Following a calculation of Perrin-Riou for one of these functions, we compute the derivative of the p-adic L-function associated to the square of the non-unit root of Frobenius at p. This generalises Greenberg's notion of [Lscr ]-invariant to these three-dimensional Galois representions.