was@modular:~/www/168/notes/2005-09-28$ sage
------------------------------------------------------------------------
  SAGE Version 0.7.5, Export Date: 2005-09-29-0607
    Distributed under the terms of the GNU General Public License (GPL)
      IPython shell -- for help type <object>?, <object>??, %magic, or help
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       sage: E = EllipticCurve([0,0,1,-1,0])
       sage: E
        _4 = Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field
	sage: P = E([0,0])
	sage: P
	 _7 = (0, 0)
	 sage: P+P
	  _8 = (1, 0)
	  sage: P+P+P
	   _9 = (-1, -1)
	   sage: P+P+P+P
	   _10 = (2, -3)
	   sage: P+P+P+P+P
	   _11 = (1/4, -5/8)
	   sage: P+P+P+P+P+P
	   _12 = (6, 14)
	   sage: 6*P
	   _13 = (6, 14)
	   sage: 7*P
	   _14 = (-5/9, 8/27)
	   sage: 8*P
	   _15 = (21/25, -69/125)
	   sage: 9*P
	   _16 = (-20/49, -435/343)
	   sage: 10*P
	   _17 = (161/16, -2065/64)
	   sage: 20*P
	   _18 = (683916417/264517696, -18784454671297/4302115807744)