 
Summary: Rational torsion in elliptic
curves and the cuspidal
subgroup
Amod Agashe
Florida State University
October 28, 2009
Slides available at:
http://www.math.fsu.edu/~agashe/math.html
1
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 finitelygenerated.
By Mazur, E(Q)tor is one of the following
15 groups:
Z/mZ, with 1 m 10 or m = 12;
Z/2Z × Z/2mZ, with 1 m 4.
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