Open AccessClassification of Elliptic Cubic Curves Over The Finite Field of Order Nineteen
Author(s) -
Emad Bakr Al-Zangana
Publication year - 2016
Publication title -
mağallaẗ baġdād li-l-ʿulūm
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.167
H-Index - 6
eISSN - 2411-7986
pISSN - 2078-8665
DOI - 10.21123/bsj.13.4.846-852
Subject(s) - mathematics , plane curve , elliptic curve , equivalence (formal languages) , schoof's algorithm , supersingular elliptic curve , order (exchange) , isomorphism (crystallography) , twisted cubic , hessian form of an elliptic curve , finite field , pure mathematics , plane (geometry) , mathematical analysis , geometry , combinatorics , quarter period , projective test , projective line , crystallography , projective space , chemistry , crystal structure , finance , economics
Plane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen, and determined if they are complete or incomplete as arcs of degree three. Also, the maximum size of a complete elliptic curve that can be constructed from each incomplete elliptic curve are given.