Elliptic Curve/Examples

Examples of Elliptic Curves

Arbitrary Example

The equation:

$y^2 = x^3 + 17$

describes an elliptic curve.

This has the rational lattice points $\tuple {-2, 3}$, $\tuple {2, 5}$, $\tuple {\dfrac 1 4, \dfrac {33} 8}$, $\tuple {-1, 4}$ and many more.