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EllipticCurves : Table of Contents
EllipticCurves
 elliptic curves and a bruteforce method for point counting
 EllPoint
bruteForceGroupOrder
 A bruteforce method to count the points on an elliptic curve in characteristic different from 2.
bruteForceGroupOrder(EllipticCurve)
 A bruteforce method to count the points on an elliptic curve in characteristic different from 2.
bruteForceGroupOrder(EllipticCurveW)
 A bruteforce method to count the points on an elliptic curve in characteristic different from 2.
bruteForceRationalPoints
 A bruteforce method to list the points on an elliptic curve.
bruteForceRationalPoints(EllipticCurve)
 A bruteforce method to list the points on an elliptic curve.
bruteForceRationalPoints(EllipticCurveW)
 A bruteforce method to list the points on an elliptic curve.
Discriminant
 A method to compute the discriminant of an elliptic curve.
Discriminant(EllipticCurve)
 A method to compute the discriminant of an elliptic curve.
Discriminant(EllipticCurveW)
 A method to compute the discriminant of an elliptic curve.
ellCurve
 A method for creating elliptic curves.
ellCurve(List,Thing)
 A method for creating elliptic curves in Weierstrass form.
ellCurve(Thing,Thing,Thing)
 A method for creating elliptic curves in short Weierstrass form.
ellCurveFromjInv
 A method to define an elliptic curve from a given jinvariant.
EllipticCurve
 The class of elliptic curves in short Weierstrass form.
EllipticCurve == EllipticCurve
EllipticCurveW
 The class of elliptic curves in Weierstrass form.
EllPoint
 The class of points of elliptic curves in short Weierstrass form.
ellPoint
 A method for defining point on an elliptic curve.
EllPoint + EllPoint
EllPoint  EllPoint
EllPoint == EllPoint
ellPoint(List,EllipticCurve)
 A method for defining point on an elliptic curve.
ellPoint(List,EllipticCurveW)
 A method for defining point on an elliptic curve.
EllPointW
 The class of points of elliptic curves in Weierstrass form.
isElliptic
 A method to check if an ideal defines an elliptic curve.
isOnEllCurve
 A method to check if a point is on an elliptic curve.
isOnEllCurve(List,EllipticCurve)
 A method to check if a point is on an elliptic curve.
isOnEllCurve(List,EllipticCurveW)
 A method to check if a point is on an elliptic curve.
jInvariant
 A method to compute the jinvariant of an elliptic curve.
jInvariant(EllipticCurve)
 A method to compute the jinvariant of an elliptic curve.
jInvariant(EllipticCurveW)
 A method to compute the jinvariant of an elliptic curve.
net(EllipticCurve)
net(EllPoint)
toShortWForm
 A method to transform an elliptic curve from Weierstrass form to short Weierstrass form.
toWeierstrass
 A method to transform a smooth plane cubic into Weierstrass form.
ZZ * EllPoint