Abstract. If $E$ is an elliptic curve, then the Galois group of the extension generated by the $n$-torsion points acts on these points. We prove a quadratic reciprocity law involving this group action. This law is an extension of the usual quadratic reciprocity law.
AMS Subject Classification
(1991): 14H52
Keyword(s):
Elliptic curve,
torsion,
Galois group,
quadratic reciprocity law
Received May 23, 2008, and in revised form August 21, 2008. (Registered under 6423/2009.)
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