Elliptic curves over totally real quartic fields not containing $\sqrt{5}$ are modular
Number Theory
2021-03-26 v1
Abstract
We prove that every elliptic curve defined over a totally real number field of degree 4 not containing is modular. To this end, we study the quartic points on four modular curves.
Cite
@article{arxiv.2103.13975,
title = {Elliptic curves over totally real quartic fields not containing $\sqrt{5}$ are modular},
author = {Josha Box},
journal= {arXiv preprint arXiv:2103.13975},
year = {2021}
}
Comments
See https://github.com/joshabox/quarticpoints/ for the Magma code used