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.)