Let $Sel^2(E/\Bbb{Q})$ be a 2-Selmer group of an elliptic curve $E/\Bbb{Q}$. For $D\in \Bbb{Z}$, let $E_D/\Bbb{Q}$ denote its quadratic twist by $D$.
It is known that
$Sel^2(E_D/\Bbb{Q})$ can be arbitrary large for fixed $E/\Bbb{Q}$ when we vary $D$.
I heard this is straight forward when $E(\Bbb{Q})[2]\neq 0$, it is straightforward.
But I couldn't come up with how to enlarge $Sel^2$ even in the case $E(\Bbb{Q})[2]\neq 0$.
Could you give me a hint or outline or sketch of this fact ?
Thank you in advance.