 
Summary: Rational torsion in elliptic
curves and the cuspidal
subgroup
Amod Agashe
Florida State University
April 27, 2006
Slides available at:
http://www.math.fsu.edu/~agashe/math.html
1
An elliptic curve E over Q is an equation of
the form y 2 = x 3 + ax + b, where a; b 2 Q and
(E) = 16(4a 3 + 27b 2 ) 6= 0, along with a
point O at innity.
Example: The graph of y 2 = x 3 x over R:
Reducing the equation modulo a prime p gives
a curve ~
E over Fp . The reduced curve can be
nonsingular { good reduction
have a node { multiplicative reduction
