Elliptic Curve

Author

Eric W. Weisstein
January 25, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheory/EllipticCurve.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/EllipticCurve.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Examples

V5

<<Graphics`ImplicitPlot`
<<Graphics`Colors`

curves={x^3-1,x^3+1,x^3-3x+3,x^3-4x,x^3-x};

Factor/@curves

Show[GraphicsArray[ImplicitPlot[#,{x,-3,3},
DisplayFunction->Identity,
PlotLabel->TraditionalForm[#],
PlotStyle->Red,AspectRatio->1,Ticks->None]&/@(y^2==#&/@curves)
]]

V7

curves={x^3-1,x^3+1,x^3-3x+3,x^3-4x,x^3-x};

Factor/@curves

GraphicsGrid[{ContourPlot[#,{x,-3,3},{y,-3,3},PlotLabel->#,ContourStyle->Red,BaseStyle->9,FrameTicks->None,Axes->True,AspectRatio->1]&/@(y^2==#&/@curves)},ImageSize->400,Spacings->-15]