Attachment 'eg.sage'

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   1 sage: E = EllipticCurve('37a1')
   2 sage: K.<a> = QuadraticField(97)
   3 sage: EK = E.change_ring(K)
   4 sage: EK1 = EK.quadratic_twist(a-3)  ## random!
   5 sage: 
   6 sage: j = EK1.j_invariant()
   7 sage: j in QQ
   8 True
   9 sage: EK2 = EllipticCurve(j=j).change_ring(K)
  10 sage: d = EK1.is_quadratic_twist(EK2); d
  11 -37/31104*a + 37/10368
  12 sage: EK1.quadratic_twist(d).is_isomorphic(EK2)
  13 True
  14 sage: EK2
  15 Elliptic Curve defined by y^2 = x^3 + (-15479341056/1369)*x + (-481469424205824/50653) over Number Field in a with defining polynomial x^2 - 97

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