Here you can plot the points of an elliptic curve under modular arithmetic (i.e. over Fp).
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 y2=x3+ax+bmodr, where
Click/tap on a point in (table or plot) to show details about that point.
| + | ∞ | (0,0) | (2,6) | (2,7) | (3,2) | (3,11) | (4,4) | (4,9) | (5,0) | (6,1) | (6,12) | (7,5) | (7,8) | (8,0) | (9,6) | (9,7) | (10,3) | (10,10) | (11,4) | (11,9) |
| ∞ | ∞ | (0,0) | (2,6) | (2,7) | (3,2) | (3,11) | (4,4) | (4,9) | (5,0) | (6,1) | (6,12) | (7,5) | (7,8) | (8,0) | (9,6) | (9,7) | (10,3) | (10,10) | (11,4) | (11,9) |
| (0,0) | (0,0) | ∞ | (7,5) | (7,8) | (9,7) | (9,6) | (10,3) | (10,10) | (8,0) | (11,9) | (11,4) | (2,6) | (2,7) | (5,0) | (3,11) | (3,2) | (4,4) | (4,9) | (6,12) | (6,1) |
| (2,6) | (2,6) | (7,5) | (9,7) | ∞ | (11,4) | (7,8) | (8,0) | (6,1) | (10,10) | (9,6) | (4,4) | (3,2) | (0,0) | (4,9) | (2,7) | (6,12) | (5,0) | (11,9) | (10,3) | (3,11) |
| (2,7) | (2,7) | (7,8) | ∞ | (9,6) | (7,5) | (11,9) | (6,12) | (8,0) | (10,3) | (4,9) | (9,7) | (0,0) | (3,11) | (4,4) | (6,1) | (2,6) | (11,4) | (5,0) | (3,2) | (10,10) |
| (3,2) | (3,2) | (9,7) | (11,4) | (7,5) | (4,4) | ∞ | (10,10) | (3,11) | (6,1) | (7,8) | (5,0) | (6,12) | (2,6) | (11,9) | (0,0) | (10,3) | (4,9) | (9,6) | (8,0) | (2,7) |
| (3,11) | (3,11) | (9,6) | (7,8) | (11,9) | ∞ | (4,9) | (3,2) | (10,3) | (6,12) | (5,0) | (7,5) | (2,7) | (6,1) | (11,4) | (10,10) | (0,0) | (9,7) | (4,4) | (2,6) | (8,0) |
| (4,4) | (4,4) | (10,3) | (8,0) | (6,12) | (10,10) | (3,2) | (9,6) | ∞ | (7,8) | (2,6) | (6,1) | (5,0) | (11,4) | (2,7) | (9,7) | (4,9) | (3,11) | (0,0) | (11,9) | (7,5) |
| (4,9) | (4,9) | (10,10) | (6,1) | (8,0) | (3,11) | (10,3) | ∞ | (9,7) | (7,5) | (6,12) | (2,7) | (11,9) | (5,0) | (2,6) | (4,4) | (9,6) | (0,0) | (3,2) | (7,8) | (11,4) |
| (5,0) | (5,0) | (8,0) | (10,10) | (10,3) | (6,1) | (6,12) | (7,8) | (7,5) | ∞ | (3,2) | (3,11) | (4,9) | (4,4) | (0,0) | (11,4) | (11,9) | (2,7) | (2,6) | (9,6) | (9,7) |
| (6,1) | (6,1) | (11,9) | (9,6) | (4,9) | (7,8) | (5,0) | (2,6) | (6,12) | (3,2) | (4,4) | ∞ | (3,11) | (10,10) | (9,7) | (8,0) | (2,7) | (7,5) | (11,4) | (0,0) | (10,3) |
| (6,12) | (6,12) | (11,4) | (4,4) | (9,7) | (5,0) | (7,5) | (6,1) | (2,7) | (3,11) | ∞ | (4,9) | (10,3) | (3,2) | (9,6) | (2,6) | (8,0) | (11,9) | (7,8) | (10,10) | (0,0) |
| (7,5) | (7,5) | (2,6) | (3,2) | (0,0) | (6,12) | (2,7) | (5,0) | (11,9) | (4,9) | (3,11) | (10,3) | (9,7) | ∞ | (10,10) | (7,8) | (11,4) | (8,0) | (6,1) | (4,4) | (9,6) |
| (7,8) | (7,8) | (2,7) | (0,0) | (3,11) | (2,6) | (6,1) | (11,4) | (5,0) | (4,4) | (10,10) | (3,2) | ∞ | (9,6) | (10,3) | (11,9) | (7,5) | (6,12) | (8,0) | (9,7) | (4,9) |
| (8,0) | (8,0) | (5,0) | (4,9) | (4,4) | (11,9) | (11,4) | (2,7) | (2,6) | (0,0) | (9,7) | (9,6) | (10,10) | (10,3) | ∞ | (6,12) | (6,1) | (7,8) | (7,5) | (3,11) | (3,2) |
| (9,6) | (9,6) | (3,11) | (2,7) | (6,1) | (0,0) | (10,10) | (9,7) | (4,4) | (11,4) | (8,0) | (2,6) | (7,8) | (11,9) | (6,12) | (4,9) | ∞ | (3,2) | (10,3) | (7,5) | (5,0) |
| (9,7) | (9,7) | (3,2) | (6,12) | (2,6) | (10,3) | (0,0) | (4,9) | (9,6) | (11,9) | (2,7) | (8,0) | (11,4) | (7,5) | (6,1) | ∞ | (4,4) | (10,10) | (3,11) | (5,0) | (7,8) |
| (10,3) | (10,3) | (4,4) | (5,0) | (11,4) | (4,9) | (9,7) | (3,11) | (0,0) | (2,7) | (7,5) | (11,9) | (8,0) | (6,12) | (7,8) | (3,2) | (10,10) | (9,6) | ∞ | (6,1) | (2,6) |
| (10,10) | (10,10) | (4,9) | (11,9) | (5,0) | (9,6) | (4,4) | (0,0) | (3,2) | (2,6) | (11,4) | (7,8) | (6,1) | (8,0) | (7,5) | (10,3) | (3,11) | ∞ | (9,7) | (2,7) | (6,12) |
| (11,4) | (11,4) | (6,12) | (10,3) | (3,2) | (8,0) | (2,6) | (11,9) | (7,8) | (9,6) | (0,0) | (10,10) | (4,4) | (9,7) | (3,11) | (7,5) | (5,0) | (6,1) | (2,7) | (4,9) | ∞ |
| (11,9) | (11,9) | (6,1) | (3,11) | (10,10) | (2,7) | (8,0) | (7,5) | (11,4) | (9,7) | (10,3) | (0,0) | (9,6) | (4,9) | (3,2) | (5,0) | (7,8) | (2,6) | (6,12) | ∞ | (4,4) |
(c) Sascha Grau, 2011, 2017