Formal Groups and Invariant Differentials of Elliptic Curves

Abstract

In this paper, we find a power series expansion of the invariant differential ${\omega }_E$ of an elliptic curve $E$ defined over $\mathbb{Q}$, where $E$ is described by certain families of Weierstrass equations. In addition, we introduce several congruence relations satisfied by the trace of the Frobenius endomorphism of $E$.

10 pages