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Mat. Tr., 2005, Volume 8, Number 1, Pages 122–134 (Mi mt57)  

Behavior of Arithmetic Invariants for a Class of Elliptic Curves in Cyclotomic $\Gamma$-Extensions

I. S. Rakhimov

National University of Uzbekistan named after M. Ulugbek

Abstract: We study the behavior of the main arithmetic invariants of elliptic curves with complex multiplication in cyclotomic $\Gamma$-extensions. We consider the curves of CM-type which are defined over the field of rational numbers and possess nondegenerate nonsupersingular reduction modulo a prime $p$, where $p\ne 2$.

Key words: elliptic curve, arithmetic invariants, $\Gamma$-extension, the Tate module.

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Bibliographic databases:

UDC: 512.7
Received: 08.07.2002

Citation: I. S. Rakhimov, “Behavior of Arithmetic Invariants for a Class of Elliptic Curves in Cyclotomic $\Gamma$-Extensions”, Mat. Tr., 8:1 (2005), 122–134

Citation in format AMSBIB
\Bibitem{Rak05}
\by I.~S.~Rakhimov
\paper Behavior of Arithmetic Invariants for a~Class of Elliptic Curves in Cyclotomic $\Gamma$-Extensions
\jour Mat. Tr.
\yr 2005
\vol 8
\issue 1
\pages 122--134
\mathnet{http://mi.mathnet.ru/mt57}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1955024}
\zmath{https://zbmath.org/?q=an:1077.11042}
\elib{http://elibrary.ru/item.asp?id=9535716}


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