We prove Getzler’s claims about the cohomology of the moduli space of stable curves of genus one, that is, that the even cohomology ring is spanned by the strata classes and that all relations between these classes follow from the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) relation and Getzler’s relation. In particular, the even cohomology ring is isomorphic to the tautological ring.
"The structure of the tautological ring in genus one." Duke Math. J. 163 (4) 777 - 793, 15 March 2014. https://doi.org/10.1215/00127094-2429916