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Congruence class bias and the Lang–Trotter conjecture for families of elliptic curves

Seraphim Jarov, Alex Khadra and Nahid Walji

Vol. 17 (2024), No. 4, 569–592
Abstract

For various families of elliptic curves over the integers, we obtain distribution results towards the Lang–Trotter conjecture on average. We demonstrate the existence of a congruence class bias in this context, and then investigate this further computationally.

Keywords
elliptic curves, traces of Frobenius, Lang–Trotter conjecture
Mathematical Subject Classification
Primary: 11G05, 14H52
Secondary: 11N37
Milestones
Received: 4 April 2022
Revised: 9 May 2023
Accepted: 15 May 2023
Published: 2 October 2024

Communicated by Bjorn Poonen
Authors
Seraphim Jarov
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada
Alex Khadra
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada
Nahid Walji
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada