A torsion point on an elliptic curve 
is a point 
of finite order in the group of points of 
. Equivalently, ![[n]P=O](/https/mathworld.wolfram.com/images/equations/TorsionPoint/Inline4.svg)
for some positive integer 
. Over a number
field, a point is torsion if and only if its canonical
height is zero.
Torsion Point
See also
Canonical Height, Elliptic Curve, Group TorsionExplore with Wolfram|Alpha
References
Silverman, J. H. The Arithmetic of Elliptic Curves, 2nd ed. New York: Springer, 2009. https://doi.org/10.1007/978-0-387-09494-6.Cite this as:
Weisstein, Eric W. "Torsion Point." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TorsionPoint.html