The control and mechanical systems of an embodied agent should be tightly coupled so that useful functionalities such as adaptivity can emerge. This indicates that the mechanical system as well as the control system should be capable of a certain level of "computation" for generating the behavior. However, the extent to which "computational offloading" from the control system to the mechanical system should be achieved requires further clarification. In order to effectively consider this, we herein focus on a passive dynamic running biped whose behavior is generated purely by its mechanical system and investigate how the body's properties influence the resulting behavior. Through numerical simulations, we have found that two elastic parameters, namely, leg spring constant and hip coil spring constant, play a crucial role as to which of various kinds of stable gait patterns are generated. To the best of our knowledge, this has not previously been addressed. The results obtained are expected to shed new light on the extent to which the mechanical system in an embodied agent should be capable of generating the behavior.