EllipticCurves -- elliptic curves and a brute-force method for point counting
Description
This package defines classes for elliptic curves, points on elliptic curves, and related methods.
Version
This documentation describes version 0.1 of EllipticCurves.
Source code
The source code from which this documentation is derived is in the file EllipticCurves.m2.
Exports
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Types
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EllipticCurve -- The class of elliptic curves in short Weierstrass form.
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EllipticCurveW -- The class of elliptic curves in Weierstrass form.
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EllPoint -- The class of points of elliptic curves in short Weierstrass form.
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EllPointW -- The class of points of elliptic curves in Weierstrass form.
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Functions and commands
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bruteForceGroupOrder -- A brute-force method to count the points on an elliptic curve in characteristic different from 2.
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bruteForceRationalPoints -- A brute-force method to list the points on an elliptic curve.
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Discriminant -- A method to compute the discriminant of an elliptic curve.
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ellCurve -- A method for creating elliptic curves.
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ellCurveFromjInv -- A method to define an elliptic curve from a given j-invariant.
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ellPoint -- A method for defining point on an elliptic curve.
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isElliptic -- A method to check if an ideal defines an elliptic curve.
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isOnEllCurve -- A method to check if a point is on an elliptic curve.
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jInvariant -- A method to compute the j-invariant of an elliptic curve.
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toShortWForm -- A method to transform an elliptic curve from Weierstrass form to short Weierstrass form.
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toWeierstrass -- A method to transform a smooth plane cubic into Weierstrass form.
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Methods