THE NUMBER OF POINTS ON ELLIPTIC CURVES E0a3:y2=x3+a3 OVER Fp MOD 24

• Journal title : Honam Mathematical Journal
• Volume 31, Issue 3,  2009, pp.437-449
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2009.31.3.437
Title & Authors
THE NUMBER OF POINTS ON ELLIPTIC CURVES E0a3:y2=x3+a3 OVER Fp MOD 24
You, Soon-Ho; Park, Hwa-Sin; Kim, Hyun;

Abstract
In this paper, we calculate the number of points on elliptic curves $\small{E^{a^3}_0:y^2=x^3+a^3}$ over $\small{{\mathbb{F}}_p}$ mod 24 and $\small{E^b_0:y^2=x^3+b}$ over $\small{{\mathbb{F}}_p}$ mod 6, where b is cubic non-residue in $\small{{\mathbb{F}}^*_p}$. For example, if p $\small{{\equiv}}$ 1 (mod 12) is a prime, and a and a(2t - 3) are quadratic residues modulo p with $\small{3t^2{\equiv}1}$ (mod p), then the number of points in $\small{E^{a^3}_0:y^2=x^3+a^3}$ is congruent to 0 modulo 24.
Keywords
elliptic curves;
Language
English
Cited by
1.
REMARK OF Pi,k ON ELLIPTIC CURVES AND APPLICATION FOR MANCHESTER CODING,;;

호남수학학술지, 2011. vol.33. 2, pp.153-161
2.
THE NUMBER OF POINTS ON ELLIPTIC CURVES y2 = x3 + Ax AND y2 = x3 + B3 MOD 24,;;

대한수학회논문집, 2013. vol.28. 3, pp.433-447
1.
REMARK OF Pi,kON ELLIPTIC CURVES AND APPLICATION FOR MANCHESTER CODING, Honam Mathematical Journal, 2011, 33, 2, 153
2.
THE NUMBER OF POINTS ON ELLIPTIC CURVES y2= x3+ Ax AND y2= x3+ B3MOD 24, Communications of the Korean Mathematical Society, 2013, 28, 3, 433
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