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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| 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 |
| 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 |
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