On the units generated by Weierstrass forms
LMS JOURNAL OF COMPUTATION AND MATHEMATICS, vol.17, pp.303-313, 2014 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 17
- Publication Date: 2014
- Doi Number: 10.1112/s1461157014000163
- Journal Name: LMS JOURNAL OF COMPUTATION AND MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.303-313
- Open Archive Collection: AVESIS Open Access Collection
- Middle East Technical University Affiliated: Yes
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.