Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs

Autor:	Arpin, Sarah
Rok vydání:	2022
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	In this paper, we add the information of level structure to supersingular elliptic curves and study these objects with the motivation of isogeny-based cryptography. Supersingular elliptic curves with level structure map to Eichler orders in a quaternion algebra, just as supersingular elliptic curves map to maximal orders in a quaternion algebra via the classical Deuring correspondence. We study this map and the Eichler orders themselves. We also look at isogeny graphs of supersingular elliptic curves with level structure, and how they relate to graphs of Eichler orders. Comment: Updated figure on page 21
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.03531 Zobrazit plný text záznamu View this record from Arxiv