5 papers · 1 filter
Distinguishing elliptic curves modulo and identifying images of product representations
Jessica Bennett, Jeffrey Hatley, Sasha Kononova +3
Given two elliptic curves defined over and a rational prime , we study the product of their residual Galois representations. Using Goursat's lemma, we explicitly en…
Elliptic curves of conductor , quadratic twists, and Watkins' conjecture
Jeffrey Hatley, Debanjana Kundu
Let be an elliptic curve. By the modularity theorem, it admits a surjection from a modular curve , and the minimal degree among such…
On a conjecture of Mazur predicting the growth of Mordell--Weil ranks in -extensions
Rylan Gajek-Leonard, Jeffrey Hatley, Debanjana Kundu +1
Let be an odd prime. We study Mazur's conjecture on the growth of the Mordell--Weil ranks of an elliptic curve over -extensions of an imaginary qua…
Iwasawa theory and ranks of elliptic curves in quadratic twist families
Jeffrey Hatley, Anwesh Ray
We study the distribution of ranks of elliptic curves in quadratic twist families using Iwasawa-theoretic methods, contributing to the understanding of Goldfeld's conjecture. Given…
Statistics for Anticyclotomic Iwasawa Invariants of Elliptic Curves
Jeffrey Hatley, Debanjana Kundu, Anwesh Ray
We study the average behaviour of the Iwasawa invariants for Selmer groups of elliptic curves, considered over anticyclotomic -extensions in both the definite and ind…