An energy-based discontinuous Galerkin discretization of the elastic wave equation in second order form. We present an application of our general formulation [SIAM J. Numer. Anal. 53, No. 6, 2705--2726 (2015; Zbl 1330.65145)] to construct energy based, arbitrary order accurate, discontinuous Galerkin spatial discretizations of the linear elastic wave equation. The resulting methods are stable and, depending on the choice of numerical flux, conserve or dissipate the elastic energy. The performance of the method is demonstrated for problems with manufactured and exact solutions. Applications to more realistic problems are also presented. Implementations of the methods are freely available at url{https://bitbucket.org/appelo/dg_dath_elastic_v1.0/src/master/}.