GALOIS STRUCTURES OF DEFINING FIELDS OF FAMILIES OF ELLIPTIC CURVES WITH CYCLIC TORSION

Abstract

The author with C. H. Kim and Y. Lee constructed infinite families of elliptic curves over cubic number fields K with prescribed torsion groups which occur infinitely often. In this paper, we examine the Galois structures of such cubic number fields K for the families of elliptic curves with cyclic torsion.

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