Evaluate
WOLFRAM|DEMONSTRATIONS PROJECT

Rational Points on an Elliptic Curve

​
P
Q
P = (-
11532
361
,
53940
6859
)
Q = (
1452
169
,-
97020
2197
)
R = (-4,-28)
-40
-30
-20
-10
10
20
30
-200
-100
100
200
P
Q
R

On an elliptic curve, if a line through two rational points P and Q intersects the curve again at R, then R is another rational point. This property is fundamental in number theory.