161001(2)

Ruby


p を法とする楕円曲線上の点の数(3)

y^2 + y = x^3 - x^2 - 40x - 221,
y^2 + y = x^3 - x^2 - 1250x + 31239,
y^2 + y = x^3 - x^2 - 946260x + 354609639

これらについて、p を法とする楕円曲線上の点の数を求め、
それぞれが一致することを確認してみた。

y^2 + y = x^3 - x^2 - 7x + 10,
y^2 + y = x^3 - x^2 - 887x - 10143

またこれらについても、p を法とする楕円曲線上の点の数を求め、
それぞれが一致することを確認してみた。

require 'prime'

def A(a3, a2, a4, a6, n)
  ary = []
  Prime.take(n).each{|p|
    a = Array.new(p, 0)
    (0..p - 1).each{|i| a[(i * i + a3 * i) % p] += 1}
    ary << (0..p - 1).inject(0){|s, i| s + a[(i * i * i + a2 * i * i + a4 * i + a6) % p]}
  }
  ary
end

n = 500
p ary = A(1, -1, -40, -221, n)
p ary == A(1, -1,   -1250,     31239, n)
p ary == A(1, -1, -946260, 354609639, n)

p ary = A(1, -1, -7, 10, n)
p ary == A(1, -1, -887, -10143, n)

出力結果
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true
true
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true