kummer-notes-code

Notes and code from my early research in Kummer Theory for Elliptic Curves.
git clone https://git.tronto.net/kummer-notes-code
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quadratic_class_number.sage (425B)

      1 # Determines the proportion of real quadratic fields with odd class number.
      2 def f(B):
      3     sqf = [ b for b in range(2,B) if b%4==1 and is_squarefree(b) ]
      4     total_odd = 0
      5 
      6     R.<x> = PolynomialRing(QQ)
      7     for a in sqf:
      8         if NumberField( x^2 - a, 'c' ).class_number() % 2 == 1:
      9             total_odd += 1
     10 
     11     print "=1 mod 4 squarefree integers up to", B, ": ", len(sqf)
     12     print "With odd class number:", total_odd