Rational points on elliptic curves y(2)=x(3)+a(3) in F-P where p equivalent to 1 (mod 6) is prime

Demirci M., Soydan G., Cangül İ. N.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, cilt.37, ss.1483-1491, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1216/rmjm/1194275930
  • Dergi Adı: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1483-1491
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

In this work, we consider the rational points on elliptic curves over finite fields F-p. We give results concerning the number of points on the elliptic curve y(2) equivalent to x(3) + a(3) (mod p) where p is a prime congruent to 1 modulo 6. Also some results are given on the sum of abscissae of these points. We give the number of solutions to y(2) equivalent to x(3) + a(3) (mod p), also given in [1, page 174], this time by means of the quadratic residue character, in a different way, by using the cubic residue character. Using the Weil conjecture, one can generalize the results concerning the number of points in F-p to F(p)r.