The noble elements constitute the simplest group of atoms. At low temperatures or high pressures, they freeze into the face-centered cubic (fcc) crystal structure (except helium). This paper investigates neon, argon, krypton, and xenon by molecular dynamics using the simplified atomic potentials recently proposed by Deiters and Sadus [J. Chem. Phys. 150, 134504 (2019)], which are parameterized using data from accurate ab initio quantum-mechanical calculations by the coupled-cluster approach at the single-double-triple level. We compute the fcc freezing lines and find good agreement with the empirical values. At low pressures, predictions are improved by including many-body corrections. Hidden scale invariance of the potential-energy function is established by showing that mean-squared displacement and the static structure factor are invariant along the lines of constant excess entropy (isomorphs). The isomorph theory of melting [Pedersen et al., Nat. Commun. 7, 12386 (2016)] is used to predict from simulations at a single state point the freezing line's shape, the entropy of melting, and the Lindemann parameter of the crystal at melting. Finally, our results suggest that the body-centered cubic crystal is the thermodynamically stable phase at high pressures.