On the units generated by Weierstrass forms


KÜÇÜKSAKALLI Ö.

LMS JOURNAL OF COMPUTATION AND MATHEMATICS, cilt.17, ss.303-313, 2014 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 17
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1112/s1461157014000163
  • Dergi Adı: LMS JOURNAL OF COMPUTATION AND MATHEMATICS
  • Sayfa Sayısı: ss.303-313

Özet

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.