The well-known and potentially disruptive plasma 'current rise' instabilities are studied as a function of the plasma shape in the Tokamak a a Configuration Variable (TCV). Disruptions typically occur in quasi-circular plasmas at q(a) - 3 in both non-sawtoothing and sawtoothing discharges with peaked current profiles. The perturbations in the plasma parameters before disruption are characterized, and the main unstable modes identified as coupled m/n = 2/1 and 3/2 rotating tearing modes. In the early phase, coupling between 3/1 and 2/1 modes is found to play a major role in determining whether or not the disruption will occur. Plasma cross section shaping is observed to reduce or to completely stabilize the disruptive mode and is regularly used in TCV operation as a tool for safe initial current ramp-up. Plasma elongation, positive and negative triangularity prevent the growth of a large 2/1 mode at q(a) - 3, thus reducing or even suppressing the disruptions. We also attempt an interpretation of the experimental results. Calculations of the tearing-mode stability parameter triangle' using the experimental plasma equilibria suggest the dominant role of toroidal mode coupling in the destabilization of the m/n = 2/1 mode in quasi-circular TCV plasmas. The effect of shaping on the reconstructed current profile and tearing stability is then considered. The analysis shows a destabilising trend with elongation and triangularity in contrast with the experiment. Other stabilizing mechanisms are discussed and shown to potentially contribute to the safe crossing of q(a) = 3 in shaped plasmas.