CoCalc Public Fileswww / 168 / notes / 2005-09-28 / sage-find-points-on-curve.txtOpen with one click!
Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
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[email protected]:~/www/168/notes/2005-09-28$ sage
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SAGE Version 0.7.5, Export Date: 2005-09-29-0607
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Distributed under the terms of the GNU General Public License (GPL)
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IPython shell -- for help type <object>?, <object>??, %magic, or help
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sage: E = EllipticCurve([0,0,1,-1,0])
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sage: E
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_4 = Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field
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sage: P = E([0,0])
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sage: P
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_7 = (0, 0)
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sage: P+P
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_8 = (1, 0)
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sage: P+P+P
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_9 = (-1, -1)
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sage: P+P+P+P
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_10 = (2, -3)
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sage: P+P+P+P+P
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_11 = (1/4, -5/8)
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sage: P+P+P+P+P+P
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_12 = (6, 14)
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sage: 6*P
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_13 = (6, 14)
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sage: 7*P
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_14 = (-5/9, 8/27)
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sage: 8*P
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_15 = (21/25, -69/125)
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sage: 9*P
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_16 = (-20/49, -435/343)
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sage: 10*P
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_17 = (161/16, -2065/64)
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sage: 20*P
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_18 = (683916417/264517696, -18784454671297/4302115807744)
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