THE NUMBER OF POINTS ON ELLIPTIC CURVES y2

Title & Authors
THE NUMBER OF POINTS ON ELLIPTIC CURVES y2
Jeon, Wonju; Kim, Daeyeoul;

Abstract
In this paper, we calculate the number of points on elliptic curves $y^2 Keywords congruence;elliptic curve; Language English Cited by References 1. I. F. Blake, G. Seroussi, and N. P. Smart, Elliptic Curves in Cryptography, Reprint of the 1999 original. London Mathematical Society Lecture Note Series, 265. Cambridge University Press, Cambridge, 2000. 2. B. M. Brewer, On certain character sums, Trans. Amer. Math. Soc. 99 (1961), 241-245. 3. M. Demirci, G. Soydan, and I. N. Cangul, Rational points on elliptic curves E :$y^2=x^3+a^3$in$\mathbb{F}_p$where$p{\equiv}1$(mod 6) is prime, Rocky Mountain J. Math. 37 (2007), no. 5, 1483-1491. 4. I. Inam, O. Bizim, and I. N. Cangul, Rational points on Frey elliptic curves E :$y^2=x^3-n^2x$, Adv. Stud. Contemp. Math. (Kyungshang) 14 (2007), no. 1, 69-76. 5. I. Inam, G. Soydan, M. Demirci, O. Bizim, and I. N. Cangul, Corrigendum on "The number of points on elliptic curves E :$y^2=x^3$+cx over$\mathbb{F}_p$mod 8", Commun. Korean Math. Soc. 22 (2007), no. 2, 207-208. 6. K. Ireland and M. Rosen A Classical Introduction to Mordern Number Theory, Springer-Verlag, 1981. 7. A. W. Knapp, Elliptic Curves, Princeton Uinversity Press, New Jersey 1992. 8. H. Park, D. Kim, and E. Lee The number of points on elliptic curves E :$y^2=x^3$+ cx over$\mathbb{F}_p$mod 8, Commun. Korean Math. Soc. 18 (2003), no. 1, 31-37. 9. H. Park, S. You, H. Park, D. Kim, and H. Kim The number of points on elliptic curves$E_A^0$:$y^2=x^3$+ Ax over$\mathbb{F}_p$mod 24, Honam Math. J. 34 (2012), no.1, 93-101. 10. A. R. Rajwade, A note on the number of solutions$N_p$of the congruence$y^2{\equiv}x^3$-Dx (mod p), Proc. Cambfidge Philos. Soc. 67 (1970), 603-605. 11. R. Schoof, Counting points on elliptic curves over finite fields, J. Theor. Nombres Bordeaux 7 (1995), no. 1, 219-254. 12. J. H. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, New York, 1986. 13. Z. H. Sun, Supplements to the theory of quartic residues, Acta Arith. 97 (2001), no. 4, 361-377. 14. B. A. Venkov, Elementary Number Theory, translated form the Russian and edited by H. Alderson, Wolters-Noordhoff, Groningen, 1970. 15. A. Weil, Sur les courbes algebriques et les varietes qui s'en deduisent, Hermann, Paris, 1948. 16. S. You, H. Park, and H. Kim The Number of points on elliptic curves$E_0^a\;^3$:$y^2=x^3+a^3b$over$\mathbb{F}_p\$ mod 24, Honam Math. J. 31 (2009), no. 3, 437-449.