On the classification of Mori contractions: the case of an elliptic curve

We study three-dimensional Mori contractions $f\colon X\to Z$. It is proved that in a “good” model $(\overline{X},\overline{S})$ there are no elliptic components of $\operatorname{Diff}_{\overline{S}}$ with coefficients $\geqslant 6/7$.