Density transition (or shock-front) injection is a technique to obtain high quality electron beams in laser wakefield acceleration. This technique, which requires no additional laser pulse, is easy to implement and is receiving increasing interest. In addition to its performances, its setup realized with a blade inserted in a gas jet allows a certain flexibility in controlling the density transition shape, whose effects on the beam quality have been studied theoretically and experimentally. We report the results of particle-in-cell simulations where the laser energy is systematically varied for different shapes of the density transition. Our study shows how the laser energy affects the injection process, increasing the injected charge and influencing the other beam characteristics (e.g. energy and duration).