.NET library for studying and working with elliptic curves

EllipticCurves is a small C# library for studying and working with elliptic curves. It provides functionality to compute and explore:

• coefficients and group structure,
• discriminant and j-invariant,
• torsion/rational/integral points,
• short and minimal Weierstrass model,
• algebraic/analytic ranks,
• LMFDB label/url,
• conductor, etc.

You can build EllipticCurves from sources or install to your own project using nuget package manager.

C# interface

using EllipticCurves;

To get started with EllipticCurves it is recommended to take a look at the example project.
Here are some results for the elliptic curve: Y^2 = X^3 - 17X^2 + 72X.

E: y^2 = x^3 - 17*x^2 + 72*x
Short Weierstrass: y^2 = x^3 - 73/3*x + 1190/27
Torsion: Z/2Z x Z/4Z
b2 = -68
b4 = 144
b6 = 0
b8 = -5184
D  = 82944
c4 = 1168
c6 = -38080
j  = 1556068/81
Torsion points:
O
(0, 0)
(8, 0)
(9, 0)
(6, 6)
(6, -6)
(12, 12)
(12, -12)
LMFDB: 48.a3
Url: https://www.lmfdb.org/EllipticCurve/Q/48.a3/
Minimal Weirstrass model: y^2 = x^3 + x^2 - 24*x + 36
Torsion: Z/2Z x Z/4Z
Rank(E) = 0
Analytic rank(E) = 0
Cond(E) = 48
Isomorphic to E: True

MIT