What is known and not known about rational points of modular curves? What are some good references?



Rational points of modular curves
Dear Dick,


I am going to interpret *rational points* to mean points over $\mathbb Q$.


Given this,
Mazur's *Eisenstein ideal* paper, his *rational isogenies* paper, and various surveys
he wrote around that time (mid-to-late 1970s) give a good description (and also prove
the most of the key results). 


Ogg also wrote surveys in the early 70s, making conjectures which Mazur then proved,
which are very helpful. You'll easily find them on mathscinet (as you will with Mazur's 
papers and surveys).


Best wishes,


Matt


