Breakup of inverse golden mean shearless tori in the two-frequency standard nontwist map

► We study the breakup of shearless invariant tori with inverse golden mean winding number in an area-preserving nontwist map perturbed by two harmonics. ► Torus breakup is studied using Greeneʼs residue criterion. ► Symmetry of the map (or lack of) is found to affect the details of the breakup.