ON MORDELL-WEIL LATTICES OF TYPE D5

We establish the analogue for D5 of the theory of algebraic equation of type E(r) (T. SHIODA: Construction of elliptic curves with high rank via the invariants of the Weyl groups, J. Math. Soc. Japan 43, 1991, No. 4, 673-719), which is one of the results of the theory of Mordell-Weil lattices. As an application, we give a method of constructing an elliptic curve over Q(t) with rank 5, together with explicit generators of the Mordell-Weil group.