  We prove an analogue of the Brauer-Siegel theorem for the Legendre elliptic
curves over $\mathbb{F}_q(t)$. More precisely, if $d$ is an integer coprime to
$q$, we denote by $E_d$ the elliptic curve with model $y^2=x(x+1)(x+t^d)$ over
$K=\mathbb{F}_q(t)$. We give an asymptotic estimate of the product of the order
of the Tate-Shafarevich group of $E_d$ (which is known to be finite) with its
N\'eron-Tate regulator, in terms of the exponential differential height of
$E_d$, as $d\to\infty$.
