호남수학학술지 (Honam Mathematical Journal)

  • 제34권1호
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  • Pages.93-101
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  • 2012
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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THE NUMBER OF POINTS ON ELLIPTIC CURVES EA0:y2=x3+Ax OVER $\mathbb{F}$p MOD 24

  • Park, Hwa-Sin (Department of Mathematics, Chonbuk National University) ;
  • You, Soon-Ho (Department of Mathematics, Chonbuk National University) ;
  • Kim, Dae-Yeoul (Division of Fusion and Convergence of Mathematical Sciences, National Institute for Mathematical Sciences) ;
  • Kim, Min-Hee (Department of Mathematics, Chonbuk National University)
  • 투고 : 2011.12.29
  • 심사 : 2012.02.07
  • 발행 : 2012.03.25
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초록

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.

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참고문헌

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피인용 문헌

  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