Summary: Rational torsion in elliptic
curves and the cuspidal
Florida State University
October 28, 2009
Slides available at:
An elliptic curve E over Q is an equation of
the form y2 = x3 + ax + b, where a, b Q and
(E) = -16(4a3 + 27b2) = 0, along with a
point O at infinity.
Example: The graph of y2 = x3 - x over R:
The abelian group E(Q) is finitely-generated.
By Mazur, E(Q)tor is one of the following
Z/mZ, with 1 m 10 or m = 12;
Z/2Z × Z/2mZ, with 1 m 4.