Weil height of a point on an elliptic curve over $\Q$ (reviewed)

The Weil height (also known as the naive height) $h(P)$ of a rational point $P$ with coordinates $(x,y)$ on an elliptic curve defined over $\Q$ is defined to be $\log\max(|a|,|b|)$ where the rational number $x$ is expressed as $x=a/b$ with $a,b$ coprime integers.