Elliptic curves with good reduction outside of the first six primes
Number Theory
2020-07-22 v1
Abstract
We present a database of rational elliptic curves, up to Q-isomorphism, with good reduction outside {2,3,5,7,11,13}. We provide a heuristic involving the abc and BSD conjectures that the database is likely to be the complete set of such curves. Moreover, proving completeness likely needs only more computation time to conclude. We present data on the distribution of various quantities associated to curves in the set. We also discuss the connection to S-unit equations and the existence of rational elliptic curves with maximal conductor.
Keywords
Cite
@article{arxiv.2007.10535,
title = {Elliptic curves with good reduction outside of the first six primes},
author = {Alex J. Best and Benjamin Matschke},
journal= {arXiv preprint arXiv:2007.10535},
year = {2020}
}
Comments
19 pages, 4 figures; the data is available at https://github.com/elliptic-curve-data/ec-data-S6