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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mod $2$ representations of elliptic curves


Authors: K. Rubin and A. Silverberg
Journal: Proc. Amer. Math. Soc. 129 (2001), 53-57
MSC (1991): Primary 11G05; Secondary 11F33
Published electronically: June 14, 2000
MathSciNet review: 1694877
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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  • 2. B. Mazur, Rational isogenies of prime degree (with an appendix by D. Goldfeld), Invent. Math. 44 (1978), no. 2, 129–162. MR 482230 (80h:14022), http://dx.doi.org/10.1007/BF01390348
  • 3. K. Rubin and A. Silverberg, Families of elliptic curves with constant mod 𝑝 representations, Elliptic curves, modular forms, & Fermat’s last theorem (Hong Kong, 1993), Ser. Number Theory, I, Int. Press, Cambridge, MA, 1995, pp. 148–161. MR 1363500 (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: http://dx.doi.org/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
Published electronically: June 14, 2000
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2000 American Mathematical Society