English

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 5\sqrt{5} is modular. To this end, we study the quartic points on four modular curves.

Keywords

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

R2 v1 2026-06-24T00:33:43.481Z