= Unramified division torsors at good primes
{title2=$v\nmid m,\quad E\text{ good at }v$}
At a prime of <good reduction of an elliptic curve> with residue characteristic not dividing $m$, multiplication by $m$ extends to a finite étale map of the smooth proper elliptic group scheme over the valuation ring. A local rational point extends to a section by properness. Its division fibre is therefore a finite étale torsor, so the <Kummer map of an elliptic curve> gives an unramified cohomology class. This bounds ramification in the <Weak Mordell-Weil theorem>.
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