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We investigate a modular $A_4$ invariant two-loop neutrino mass model in asupersymmetric framework, where we introduce new fields as minimum as possible,expecting contributions of superpartners to the neutrino masses. Wesuccessfully reproduce the neutrino oscillation data thanks to the superpartnercontributions in case of normal hierarchy, and predict several observables suchas phases and neutrino masses, concentrating on three specific regions atnearby fixed points of modulus $\tau=i,\omega,i\times \infty$, where$\omega\equiv e^{2\pi i/3}$. These points are statistically favored in fluxcompactifications of the string theory. We show several results in each thepoints by performing global $\chi^2$ analysis, and demonstrate benchmark pointswith the minimum $\chi^2$.

Radiative neutrino masses from modular $A_4$ symmetry and supersymmetry breaking