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Images of mod p Galois Representations Associated to Elliptic Curves

  • Amadeu Reverter (a1) and Núria Vila (a2)
Abstract

We give an explicit recipe for the determination of the images associated to the Galois action on p-torsion points of elliptic curves. We present a table listing the image for all the elliptic curves defined over without complex multiplication with conductor less than 200 and for each prime number p.

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References
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[1] Birch, B. and Kuyk, W. (eds.), Modular Functions of One Variable IV. Lecture Notes in Math. 476, Springer-Verlag, 1972.
[2] Mazur, B., Rational isogenies of prime degree. Invent.Math. 44 (1978), 129162.
[3] Serre, J.-P., Abelian l-Adic Representations and Elliptic Curves. W. A. Benjamin, Inc., 1968.
[4] Serre, J.-P., Propriétés galoisiennes des points d’ordre fini des courbes elliptiques. Invent.Math. 15 (1972), 259331.
[5] Serre, J.-P. and Tate, J., Good reduction of abelian varieties. Ann. of Math. 88 (1968), 492517.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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