For an elliptic curve defined over the rational numbers, it is well-known that the special value of its Hasse-Weil L-function at s=1 is a rational multiple of the real period of the elliptic curve. Inspired by work of Anderson on special values of Goss L-functions over global function fields, we investigate log-algebraic power series identities that specialize to yield this same information about the value L(E/Q,1) when it is non-vanishing. The techniques involve an analysis of the exponential and logarithm of the traditional formal group of the elliptic curve and the construction of an isomorphism, by way of the modular parametrization, between this formal group and the formal group defined by Honda for its L-function. Joint work with Huang Wei-Cheng.