The purpose of this article is to record the computation homotopy groups 3-local \(\mathrm {tmf}\) via Adams spectral sequence.

We calculate the η-localization of the motivic stable homotopy ring over C, confirming a conjecture of Guillou and Isaksen. Our approach is via the motivic Adams-Novikov spectral sequence. In fact, work of Hu, Kriz and Ormsby implies that it suffices to compute the α1localization of the classical Adams-Novikov E2-term, and this is what we do. Guillou and Isaksen also propose a pattern of differ...