## Elliptic Curves and the ABC Conjecture

In this project we study Belyi maps for elliptic curves and their use as a source of abc triples. While we are not necessarily expecting to produce record abc triples in this manner, this method is a potential source of interesting sequences of triples. We intend to investigate limit points for such sequences, varying the elliptic curve and the base point. This project will require using and developing functionality for Belyi maps, factoring and potentially elliptic curve divisibility sequences. Some useful references for the abc conjecture can be found here: http://en.wikipedia.org/wiki/Abc_conjecture

Primary reference: http://myweb.lmu.edu/lkhadjavi/BelyiElliptic.pdf

Talk slides: Sage Days 50 slides.pdf