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# bruteForceRationalPoints(EllipticCurve) -- A brute-force method to list the points on an elliptic curve.

## Description

 i1 : E=ellCurve(3,8,GF(13)) o1 = Elliptic Curve defined by Y^2 = X^3 + 3 X + (-5)( over(GF 13 .)) o1 : EllipticCurve i2 : bruteForceRationalPoints(E) o2 = {Point ({0, 1, 0}( on the (Elliptic Curve defined by Y^2 = X^3 + 3 X + ------------------------------------------------------------------------ (-5)( over(GF 13 .))))), Point ({1, -5, 1}( on the (Elliptic Curve ------------------------------------------------------------------------ defined by Y^2 = X^3 + 3 X + (-5)( over(GF 13 .))))), Point ({1, 5, 1}( ------------------------------------------------------------------------ on the (Elliptic Curve defined by Y^2 = X^3 + 3 X + (-5)( over(GF 13 ------------------------------------------------------------------------ .))))), Point ({2, 3, 1}( on the (Elliptic Curve defined by Y^2 = X^3 + ------------------------------------------------------------------------ 3 X + (-5)( over(GF 13 .))))), Point ({2, -3, 1}( on the (Elliptic Curve ------------------------------------------------------------------------ defined by Y^2 = X^3 + 3 X + (-5)( over(GF 13 .))))), Point ({-1, 2, 1}( ------------------------------------------------------------------------ on the (Elliptic Curve defined by Y^2 = X^3 + 3 X + (-5)( over(GF 13 ------------------------------------------------------------------------ .))))), Point ({-1, -2, 1}( on the (Elliptic Curve defined by Y^2 = X^3 ------------------------------------------------------------------------ + 3 X + (-5)( over(GF 13 .))))), Point ({-4, 6, 1}( on the (Elliptic ------------------------------------------------------------------------ Curve defined by Y^2 = X^3 + 3 X + (-5)( over(GF 13 .))))), Point ({-4, ------------------------------------------------------------------------ -6, 1}( on the (Elliptic Curve defined by Y^2 = X^3 + 3 X + (-5)( ------------------------------------------------------------------------ over(GF 13 .)))))} o2 : List