Goldfeld conjecture asserts that for elliptic curve $E/\Bbb{Q}$,
$rank(E_D/\Bbb{Q})=0$ for $50%$ square free D's
$rank(E_D/\Bbb{Q})=1$ for $50%$ square free D's
$rank(E_D/\Bbb{Q})=2$ for $0％$ square free D's
My question is,
$1.$ Does this imply that only a finite number of $E_D$ have a rank greater than $2$?
$2.$ Are there any known examples of elliptic curves where this conjecture has been verified?