On the units generated by Weierstrass forms


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KÜÇÜKSAKALLI Ö.

LMS JOURNAL OF COMPUTATION AND MATHEMATICS, vol.17, pp.303-313, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17
  • Publication Date: 2014
  • Doi Number: 10.1112/s1461157014000163
  • Title of Journal : LMS JOURNAL OF COMPUTATION AND MATHEMATICS
  • Page Numbers: pp.303-313

Abstract

There is an algorithm of Schoof for finding divisors of class numbers of real cyclotomic fields of prime conductor. In this paper we introduce an improvement of the elliptic analogue of this algorithm by using a subgroup of elliptic units given by Weierstrass forms. These elliptic units which can be expressed in terms of x-coordinates of points on elliptic curves enable us to use the fast arithmetic of elliptic curves over finite fields.