Elliptic Curves over Finite Fields

Here you can plot the points of an elliptic curve under modular arithmetic (i.e. over \( \mathbb{F}_p\)).
Enter curve parameters and press 'Draw!' to get the plot and a tabulation of the point additions on this curve.

Note: Since it depends on multiplicative inverses, EC Point addition will only work for prime moduli like 2,3,5,7,11,13,17,19,23,29,31,...,109,... ;-)

Draw the elliptic curve \( y^2 = x^3+ax+b \mod r \), where

\(a\): \(b\): \(r\):

Point Detail

Table of Point Additions

(c) Sascha Grau, 2011, 2017