EllipticCurves : Table of Contents

EllipticCurves  elliptic curves and a bruteforce method for point counting


bruteForceGroupOrder  A bruteforce method to count the points on an elliptic curve in characteristic different from 2.






Discriminant  A method to compute the discriminant of an elliptic curve.



ellCurve  A method for creating elliptic curves.



ellCurveFromjInv  A method to define an elliptic curve from a given jinvariant.

EllipticCurve  The class of elliptic curves in short Weierstrass form.



EllPoint  The class of points of elliptic curves in short Weierstrass form.

ellPoint  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.



jInvariant  A method to compute the jinvariant of an elliptic curve.





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.
