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EllipticCurves :: bruteForceRationalPoints(EllipticCurve)

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

Synopsis

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