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Mod $2$ representations of elliptic curves

Author(s): K. Rubin; A. Silverberg
Journal: Proc. Amer. Math. Soc. 129 (2001), 53-57.
MSC (1991): Primary 11G05; Secondary 11F33
Posted: June 14, 2000
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Abstract:

Explicit equations are given for the elliptic curves (in characteristic $\ne 2, 3$) with mod $2$ representation isomorphic to that of a given one.

References:

1.
N. Bourbaki, Algebra II, Springer, Berlin, 1990. MR 91h:00003
2.
B. Mazur, Rational isogenies of prime degree, Invent. Math. 44 (1978), 129-162. MR 80h:14022
3.
K. Rubin, A. Silverberg, Families of elliptic curves with constant mod $p$ representations, in Conference on Elliptic Curves and Modular Forms, Hong Kong, December 18-21, 1993, Intl. Press, Cambridge, Massachusetts, 1995, pp. 148-161. MR 96j:11078
4.
-, Mod 6 representations of elliptic curves, in Automorphic Forms, Automorphic Representations, and Arithmetic, Proc. Symp. Pure Math., Vol. 66, Part 1, AMS, Providence, 1999, pp. 213-220.
5.
A. Silverberg, Explicit families of elliptic curves with prescribed mod $N$ representations, in Modular Forms and Fermat's Last Theorem, eds. Gary Cornell, Joseph H. Silverman, Glenn Stevens, Springer, Berlin, 1997, pp. 447-461. CMP 98:16

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Additional Information:

K. Rubin
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-2125 -- Department of Mathematics, Ohio State University, 231 W. 18 Avenue, Columbus, Ohio 43210-1174
Email: rubin@math.stanford.edu

A. Silverberg
Affiliation: Department of Mathematics, Ohio State University, 231 W. 18 Avenue, Columbus, Ohio 43210-1174
Email: silver@math.ohio-state.edu

DOI: 10.1090/S0002-9939-00-05539-8
PII: S 0002-9939(00)05539-8
Keywords: Elliptic curves, Galois representations, modular curves
Received by editor(s): March 23, 1999
Posted: June 14, 2000
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2000, American Mathematical Society

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