THE NUMBER OF POINTS ON ELLIPTIC CURVES EA0:y2=x3+Ax OVER $\small{\mathbb{F}}$p MOD 24

• Journal title : Honam Mathematical Journal
• Volume 34, Issue 1,  2012, pp.93-101
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2012.34.1.93
Title & Authors
THE NUMBER OF POINTS ON ELLIPTIC CURVES EA0:y2=x3+Ax OVER $\small{\mathbb{F}}$p MOD 24
Park, Hwa-Sin; You, Soon-Ho; Kim, Dae-Yeoul; Kim, Min-Hee;

Abstract
Let $\small{E_A^B}$ denote the elliptic curve $\small{E_A^B:y^2=x^3+Ax+B}$. In this paper, we calculate the number of points on elliptic curves $\small{E_A^0:y^2=x^3+Ax}$ over $\small{\mathbb{F}_p}$ mod 24. For example, if $\small{p{\equiv}1}$ (mod 24) is a prime, $\small{3t^2{\equiv}1}$ (mod p) and A(-1 + 2t) is a quartic residue modulo p, then the number of points in $\small{E_A^0:y^2=x^3+Ax}$ is congruent to 0 modulo 24.
Keywords
elliptic curves;
Language
English
Cited by
1.
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.
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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