This may be trivial but I cannot find it. Given an elliptic curve, $C$ over $R$ with chosen parametrization $R\to \mathbb{A}^5_{\mathbb{Z}}=Spec(A)$, is there a way to compute coefficients of the associated formal group law, assuming this is enough information to coordinatize it. I would assume that the coefficients are rational or at least analytic function of our parametrization, though I am not making any headway. Can anyone enlighten me on this issue?

Edit: When considering the pullback of $Spec(L)\to \mathcal{M}_{FG}$ along $\mathcal{M}_{Ell}\to \mathcal{M}_{FG}$, we get $Spec(A[b_1, b_2, ...])$ so that the zero morphism should give us a map $Spec(A)\to Spec(L)$, which should be what we want. Computation of this map though, is not clear to me.