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The author shows that the isomorphism class of a formal group over Z/pZ (resp. over Z) of finite height (resp. having reduction mod p of finite height) is determined by its characteristic polynomial. It is then proved that the formal groups associated to a large class of Dirichlet series with integer coefficients are defined over Z. Finally, these results are used to extend a theorem of Honda (Osaka J. Math. 5, 199-213 (1968), Theorem 5) to include the case of supersingular reduction at the primes 2 and 3. Let E be an elliptic curve defined over Q, and F(x, y) be a formal minimal model for E. Let G(x, y) be the formal group associated to the global L-series L(E, s) of E over Q. Honda's theorem now becomes: G(x, y) is defined over Z and is isomorphic over Z to F(x, y). [ABSTRACT FROM AUTHOR]