This work aims at investigating the role of local calcium releases (LCRs) in pacemaking. This is achieved by developing a 3D model of a single rabbit sinoatrial node cell featuring detailed membrane and calcium-clock descriptions. Secondly, single cell simulations where LCRs were prevented during the diastolic period are run to assess their effect on the cell's cycle length. Finally, two heterogeneous model cells were coupled together to study the influence of LCRs on the synchronization process. The simulations show that this model reproduces both experimental and previous models' basal rabbit sinoatrial cell action potential characteristics. Comparing simulations in control conditions with simulations where LCRs are prevented below a membrane voltage value of -30 mV shows that the latters are fundamental to trigger action potentials at a physiologic rate (+60% diastolic period prolongation without LCR), but act only in the exponential phase of diastole. Coupled cells simulations at different gap junctional resistance values show that, even if one of the two cells is not spontaneous, it can be always driven by the auto-oscillatory one. Additionally, regardless of the coupling strength, cycle length synchronization is always achieved. Overall, this work provides a useful tool to study pacemaking and gives quantitative hints on its mechanisms.