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arXiv · 1303.6706

Formal Groups and Invariant Differentials of Elliptic Curves

Mohammad Sadek
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Abstract

In this paper, we find a power series expansion of the invariant differential $ω_E$ 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 $E$.

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Mohammad Sadek. 2015-03-14. Formal Groups and Invariant Differentials of Elliptic Curves. https://doi.org/10.1017/s0004972715000295

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