The group structure of bachet elliptic curves over finite fields f-p
Date
2009
Authors
İkikardeş, Nazlı Yıldız
Journal Title
Journal ISSN
Volume Title
Publisher
Univ Miskolc Inst Math
Abstract
Bachet elliptic curves are the curves y(2) = x(3) + a(3) and, in this work, the group structure E(F-p) of these curves over finite fields F-p is considered. It is shown that there are two possible structures E(F-p) congruent to Cp+1 or E(F-p) congruent to C-n x C-nm, for m, n is an element of N; according to p equivalent to 5 (mod 6) and p equivalent to 1 (mod 6), respectively. A result of Washington is restated in a more specific way saying that if E(F-p) congruent to Z(n) x Z(n) then p equivalent to 7 (mod 12) p = n(2) -/+ n + 1.
Description
Keywords
Elliptic curves over finite fields, Rational points, Mathematics
Citation
İkikardeş, N. Y. vd. (2009). "The group structure of bachet elliptic curves over finite fields f-p". Miskolc Mathematical Notes, 10(2), 129-136.