The modular curve $\Xnd{11}$ (or $X_{\mathrm{nonsplit}}(11)$)
classifies the elliptic curves $E$ such that Galois acts on the group
of 11-torsion points of $E$ through the normaliser of a non-split
Cartan subgroup. It is known that this curve has genus 1. We give here
a parametrisation of this curve by a certain elliptic curve over $\Q$
with conductor 121. As an application, we give explicit examples of
couples of elliptic curves over $\Q$ nonisogenous over $\Q$ but
giving symplectically isomorphic modulo 11 Galois representations.