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

Park, Hwa-Sin;You, Soon-Ho;Kim, Dae-Yeoul;Kim, Min-Hee

  • Received : 2011.12.29
  • Accepted : 2012.02.07
  • Published : 2012.03.25

Abstract

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

Keywords

elliptic curves

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Cited by

  1. THE NUMBER OF POINTS ON ELLIPTIC CURVES y2= x3+ Ax AND y2= x3+ B3MOD 24 vol.28, pp.3, 2013, https://doi.org/10.4134/CKMS.2013.28.3.433