  We continue our study of the Legendre elliptic curve $y^2=x(x+1)(x+t)$ over
function fields $K_d=\mathbf{F}_p(\mu_d,t^{1/d})$. When $d=p^f+1$, we have
previously exhibited explicit points generating a subgroup $V_d$ of $E(K_d)$ of
rank $d-2$ and of finite, $p$-power index. We also proved the finiteness of
$III(E/K_d)$ and a class number formula: $[E(K_d):V_d]^2=|III(E/K_d)|$. In this
paper, we compute $E(K_d)/V_d$ and $III(E/K_d)$ explicitly as modules over
$\mathbf{Z}_p[\mathrm{Gal}(K_d/F_p(t))]$.
