Moduli of genus one curves with two marked points as a weighted blow-up

Abstract: We give an explicit description of $\overline{\mathcal{M}}{1,2}$ as a weighted blow-up of a weighted projective stack. We use this description to compute the Brauer group of $\overline{\mathcal{M}}{1,2;S}$ over any base scheme $S$ where 6 is invertible, and the integral Chow rings of $\overline{\mathcal{M}}{1,2}$ and $\mathcal{M}{1,2}$.