On the units generated by Weierstrass forms

Creative Commons License

KÜÇÜKSAKALLI Ö.

LMS JOURNAL OF COMPUTATION AND MATHEMATICS, cilt.17, ss.303-313, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1112/s1461157014000163
  • Dergi Adı: LMS JOURNAL OF COMPUTATION AND MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.303-313
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

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.