 
Summary: The modular degree,
congruence number, and
multiplicity one
Amod Agashe
Florida State University
joint work with K. Ribet and W. Stein
October 4, 2007
Slides and paper available at:
http://www.math.fsu.edu/~agashe/math.html
1
Elliptic curves
Let E be an elliptic curve over Q, i.e., an
equation of the form y2 = x3 + ax + b, where
a, b Q
Example: The graph of y2 = x3  x over R:
If p is a prime, then we can "think of" the
equation for E modulo p
Let ap(E) = 1 + p  #solutions to E mod p.
2
Modular curves and modular forms
