= Division point of an elliptic curve
{title2=$[N]Q=P$}
= Division points of an elliptic curve
{synonym}
A division point above $P$ is a point $Q$ over an <algebraic closure> satisfying $[N]Q=P$, for a specified nonzero integer $N$. Two such points differ by an $N$-<torsion point of an elliptic curve>. If the <characteristic of a field> does not divide $N$, there are $N^2$ distinct division points; in other characteristics the scheme fibre still has length $N^2$, but its geometric points can be fewer. The <unramified division torsors at good primes> control their coordinate fields over <local fields>.
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