The motivation of this question can be found in
Is it possible to say that every point $P$ in $C(ℚ)$ other than the 'basis' is of finite order?
Given the elliptic curve: $$C:y²=x³+ax+b$$
for $a,b∈ℤ$.
Let $O$ be the identity element of $C(ℚ)$. I know about the Nagell-Lutz theorem [T. Nagell, Solution de quelque problèmes dans la théorie arithmétique des cubiques planes du premier genre, Wid. Akad. Skrifter Oslo I (1935), No. 1, 1-25, E. Lutz, Sur l'equation $y²=x³-Ax-B$ dans les corps $p$-adic, J. Reine Angew. Math. 177 (1937), 238-247.] in its explicit form. However, I found a strong form of the Nagell-Lutz theorem saying that if $T∈C(ℚ)^{tors}$, then $2T=O$. I do not understand how I can obtain the formula $2T=O$ from the standard Nagell-Lutz theorem.