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FORMAL GROUPS AND INVARIANT DIFFERENTIALS OF ELLIPTIC CURVES

Part of: Curves

Published online by Cambridge University Press:  04 May 2015

MOHAMMAD SADEK
MOHAMMAD SADEK*
Affiliation:
Department of Mathematics and Actuarial Science, American University in Cairo, Egypt email [email protected]
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Abstract

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

Keywords

elliptic curvesformal groupsinvariant differentials

MSC classification

Primary: 14H52: Elliptic curves
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 1 , August 2015 , pp. 44 - 51
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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