호남수학학술지 (Honam Mathematical Journal)

  • 제31권3호
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  • Pages.437-449
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  • 2009
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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 E0a3:y2=x3+a3 OVER Fp MOD 24

  • 투고 : 2009.07.13
  • 심사 : 2009.08.21
  • 발행 : 2009.09.25
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초록

In this paper, we calculate the number of points on elliptic curves $E^{a^3}_0:y^2=x^3+a^3$ over ${\mathbb{F}}_p$ mod 24 and $E^b_0:y^2=x^3+b$ over ${\mathbb{F}}_p$ mod 6, where b is cubic non-residue in ${\mathbb{F}}^*_p$. For example, if p ${\equiv}$ 1 (mod 12) is a prime, and a and a(2t - 3) are quadratic residues modulo p with $3t^2{\equiv}1$ (mod p), then the number of points in $E^{a^3}_0:y^2=x^3+a^3$ is congruent to 0 modulo 24.

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참고문헌

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피인용 문헌

  1. REMARK OF Pi,kON ELLIPTIC CURVES AND APPLICATION FOR MANCHESTER CODING vol.33, pp.2, 2011, https://doi.org/10.5831/HMJ.2011.33.2.153
  2. 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