Integral Points of Elliptic Curve y^2 = x^3+3x

Theorem
The elliptic curve:
 * $y^2 = x^3 + 3x$

has exactly $7$ lattice points:
 * $\tuple {0, 0}, \tuple {1, \pm 2}, \tuple {3, \pm 6}, \tuple {12, \pm 42}$