On the p-th division polynomial

By using the relations between supersingular elliptic curves defined over a finite field of characteristic p > 3 and the p-th division polynomial, we present a property about the reduction modulo a prime p > 3 of the p-th division polynomial based on a heuristic argument and numerical evidence...

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Bibliographic Details
Author: González Rovira, Josep|||0000-0002-9850-1609
Format: article
Publication Date:2021
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/350608
Online Access:https://hdl.handle.net/2117/350608
https://dx.doi.org/10.1016/j.jnt.2021.06.011
Access Level:Open access
Keyword:Polynomials
Number theory
Curves, Elliptic
Polinomis
Nombres, Teoria dels
Corbes el·líptiques
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
Description
Summary:By using the relations between supersingular elliptic curves defined over a finite field of characteristic p > 3 and the p-th division polynomial, we present a property about the reduction modulo a prime p > 3 of the p-th division polynomial based on a heuristic argument and numerical evidence. We prove this property determining the p-th division polynomial of supersingular elliptic curves. As a consequence of this result, we present a criterion to discard supersingular elliptic curves