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# EllipticCurves : Table of Contents

- EllipticCurves -- elliptic curves and a brute-force method for point counting
- - EllPoint
- bruteForceGroupOrder -- A brute-force method to count the points on an elliptic curve in characteristic different from 2.
- bruteForceGroupOrder(EllipticCurve) -- A brute-force method to count the points on an elliptic curve in characteristic different from 2.
- bruteForceGroupOrder(EllipticCurveW) -- A brute-force method to count the points on an elliptic curve in characteristic different from 2.
- bruteForceRationalPoints -- A brute-force method to list the points on an elliptic curve.
- bruteForceRationalPoints(EllipticCurve) -- A brute-force method to list the points on an elliptic curve.
- bruteForceRationalPoints(EllipticCurveW) -- A brute-force 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 j-invariant.
- 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 j-invariant of an elliptic curve.
- jInvariant(EllipticCurve) -- A method to compute the j-invariant of an elliptic curve.
- jInvariant(EllipticCurveW) -- A method to compute the j-invariant 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