An analysis of $\Lambda_b^0 \rightarrow \Lambda\mu^+\mu^-$ decays at the LHCb experiment Pescatore L. Birmingham U. 2015 The branching fraction of the rare decay $\Lambda_b^0 \rightarrow \Lambda \mu^+ \mu^-$ is measured as a function of $q^2$, the square of the dimuon invariant mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb$^{-1}$, collected by the LHCb experiment. Evidence of signal is found for the first time in the $q^2$ region below the square of the J/$\psi$ mass. In the $q^2$ intervals where the signal is observed, angular distributions are studied and two forward-backward asymmetries, in the dimuon and hadronic systems, are measured for the first time. PREPRINT