The moduli space  of stable 2-pointed genus 1 curves has cyclic quotient singularities, so any Weil divisor on $\overline{M}_{1,2}$ is $\mathbb{Q}$-Cartier.

**Is one of the two boundary divisors $\Delta_{irr}$ and $\Delta_{0,2}$ of $\overline{M}_{1,2}$ Cartier ?**