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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Mod $2$ representations of elliptic curves
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by K. Rubin and A. Silverberg PDF
Proc. Amer. Math. Soc. 129 (2001), 53-57 Request permission

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
  • N. Bourbaki, Algebra. II. Chapters 4–7, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1990. Translated from the French by P. M. Cohn and J. Howie. MR 1080964
  • B. Mazur, Rational isogenies of prime degree (with an appendix by D. Goldfeld), Invent. Math. 44 (1978), no. 2, 129–162. MR 482230, DOI 10.1007/BF01390348
  • 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
  • —, 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.
  • 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.
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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
  • MR Author ID: 151435
  • Email: rubin@math.stanford.edu
  • A. Silverberg
  • Affiliation: Department of Mathematics, Ohio State University, 231 W. 18 Avenue, Columbus, Ohio 43210-1174
  • MR Author ID: 213982
  • Email: silver@math.ohio-state.edu
  • Received by editor(s): March 23, 1999
  • Published electronically: June 14, 2000
  • Communicated by: David E. Rohrlich
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 53-57
  • MSC (1991): Primary 11G05; Secondary 11F33
  • DOI: https://doi.org/10.1090/S0002-9939-00-05539-8
  • MathSciNet review: 1694877