Mod 2 representations of elliptic curves

Mod $2$ representations of elliptic curves
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Proc. Amer. Math. Soc. 129 (2001), 53-57

DOI: https://doi.org/10.1090/S0002-9939-00-05539-8

Published electronically: June 14, 2000

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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.