Bounds for Integral j -Invariants and Cartan Structures on Elliptic Curves
Classical Analysis and ODEs
2016-10-05 v1
Abstract
We bound the j -invariant of integral points on a modular curve in terms of the congruence group defining the curve. We apply this to prove that the modular curve Xsplit (p3) has no non-trivial rational point if p is a sufficiently large prime number. Assuming the GRH, one can replace p3 by p2 .
Keywords
Cite
@article{arxiv.0807.2350,
title = {Bounds for Integral j -Invariants and Cartan Structures on Elliptic Curves},
author = {Yuri Bilu and Pierre Parent},
journal= {arXiv preprint arXiv:0807.2350},
year = {2016}
}