= Prime-two torsion bound for good reduction
{title2=$\#(E_1\cap E(\mathbb Q_2)_{\mathrm{tors}})\leq2$}
For an <elliptic curve> with good reduction over $\mathbb Q_2$, let $E_1$ be the reduction kernel and $E_2$ its formal subgroup with parameter in $4\mathbb Z_2$. The <deep logarithm subgroup of a formal group> makes $E_2$ torsion-free, while $[E_1:E_2]=2$. Thus the torsion of the reduction kernel has order at most $2$. Combined with the <Hasse theorem for elliptic curves>, rational torsion of order $16$ forces bad reduction at $2$.
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