(This is a hybrid seminar. In-person participation is restricted to members of Kyoto University)

Possible structures of Mordell-Weil groups are completely classified by Oguiso and Shioda(1991). Karayayla(2011) gave a list of possible groups of surface automorphisms preserving a section.

In this note, we construct a concrete example of an elliptic surface, whose Mordell-Weil group is isomorphic to the dual lattice of root system $E_7$.
The generators of the Mordell-Weil group are specified, in terms of sections of the elliptic fibration, and in terms of automorphisms of invariant cubic curve.
The group of the automorphisms of the elliptic surface is determined.