19 citations · 45 across the 10 of their papers we have counts for
13 papers · 1 filter
Towards a classification of entanglements of Galois representations attached to elliptic curves
Harris B. Daniels, Álvaro Lozano-Robledo, Jackson S. Morrow
Let be an elliptic curve, let be a fixed algebraic closure of , and let $G_{\mathbb{Q}}=\text{Gal}(\overline{\mathbb{Q}}/\mathbb{…
An Errata for: Torsion subgroups of rational elliptic curves over the compositum of all extensions of the rational numbers
Harris B. Daniels
In [2], the author claims that the fields defined in the paper and the compositum of all extensions of coincide. The proof of this claim…
A group theoretic perspective on entanglements of division fields
Harris B. Daniels, Jackson S. Morrow
In this paper, we initiate a systematic study of entanglements of division fields from a group theoretic perspective. For a positive integer and a subgroup $G\subseteq \text{GL…
Coincidences of division fields
Harris B. Daniels, Álvaro Lozano-Robledo
Let be an elliptic curve defined over , and let be the adelic represen…
Serre's constant of elliptic curves over the rationals
Harris B. Daniels, Enrique González-Jiménez
Let be an elliptic curve without complex multiplication defined over the rationals. The purpose of this article is to define a positive integer , that we call the {\it Se…
Torsion groups of elliptic curves over the -extensions of
Michael Chou, Harris B. Daniels, Ivan Krijan +1
We determine, for an elliptic curve and for all , all the possible torsion groups , where is the $\mathbb…
On the torsion of rational elliptic curves over sextic fields
Harris B. Daniels, Enrique González-Jiménez
Given an elliptic curve with torsion subgroup we study what groups (up to isomorphism) can occur as the torsion subgroup of base-e…
Groups of generalized -type and applications to torsion subgroups of rational elliptic curves over infinite extensions of
Harris B. Daniels, Maarten Derickx, Jeffrey Hatley
Recently there has been much interest in studying the torsion subgroups of elliptic curves base-extended to infinite extensions of . In this paper, given a finite group…
Torsion subgroups of rational elliptic curves over the compositum of all extensions of the rational numbers
Harris B. Daniels
Let be an elliptic curve and let be the compositum of all extensions of whose Galois closure has Galois group isomorphic to a q…
Bounds of the rank of the Mordell-Weil group of jacobians of hyperelliptic curves
Harris B. Daniels, Álvaro Lozano-Robledo, Erik Wallace
In this article we extend work of Shanks and Washington on cyclic extensions, and elliptic curves associated to the simplest cubic fields. In particular, we give families of exampl…
On the ranks of elliptic curves with isogenies
Harris B. Daniels, Hannah Goodwillie
In recent years, the question of whether the ranks of elliptic curves defined over are unbounded has garnered much attention. One can create refined versions of this q…
Torsion subgroups of rational elliptic curves over the compositum of all cubic fields
Harris B. Daniels, Alvaro Lozano-Robledo, Filip Najman +1
Let be an elliptic curve and let be the compositum of all cubic extensions of . In this article we show that the torsion subgroup…
Elliptic curves with maximally disjoint division fields
Harris B. Daniels, Jeffrey Hatley, James Ricci
One of the many interesting algebraic objects associated to a given rational elliptic curve, , is its full-torsion representation $ρ_E:\mathrm{Gal}(\bar{\mathbf{Q}}/\mathbf{Q})\…