Mod 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

Explicit equations are given for the elliptic curves (in characteristic ) with mod representation isomorphic to that of a given one.

**1.**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****2.**B. Mazur,*Rational isogenies of prime degree (with an appendix by D. Goldfeld)*, Invent. Math.**44**(1978), no. 2, 129–162. MR**482230**, 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****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**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:
https://doi.org/10.1090/S0002-9939-00-05539-8

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