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