THE GROUP STRUCTURE OF BACHET ELLIPTIC CURVES OVER FINITE FIELDS F-p

Ikikardes N. Y., DEMİRCİ M., Soydan G., CANGÜL İ. N.

MISKOLC MATHEMATICAL NOTES, cilt.10, sa.2, ss.129-136, 2009 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 2
  • Basım Tarihi: 2009
  • Doi Numarası: 10.18514/mmn.2009.182
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.129-136
  • Anahtar Kelimeler: elliptic curves over finite fields, rational points
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.