  We construct explicit examples of E_8 lattices occurring in arithmetic for
which the natural Galois action is equal to the full group of automorphisms of
the lattice, i.e., the Weyl group of E_8. In particular, we give explicit
elliptic curves over Q(t) whose Mordell-Weil lattices are isomorphic to E_8 and
have maximal Galois action.
  Our main objects of study are del Pezzo surfaces of degree 1 over number
fields. The geometric Picard group, considered as a lattice via the negative of
the intersection pairing, contains a sublattice isomorphic to E_8. We construct
examples of such surfaces for which the action of Galois on the geometric
Picard group is maximal.
