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The Group Structure of Bachet Elliptic Curves over Finite Fields F_{p}
- Source :
- Miskolc Mathematical Notes, Vol. 10 (2009), No. 2, 129-136
- Publication Year :
- 2011
-
Abstract
- Bachet elliptic curves are the curves y^2=x^3+a^3 and in this work the group structure E(F_{p}) of these curves over finite fields F_{p} is considered. It is shown that there are two possible structures E(F_{p}){\cong}C_{p+1} or E(F_{p}){\cong}C_{n}{\times}C_{nm}, for m,n{\in}{\mathbb{N}}, according to p{\equiv}5 (mod6) and p{\equiv}1 (mod6), respectively. A result of Washington is restated in a more specific way saying that if E(F_{p}){\cong}Z_{n}{\times}Z_{n}, then p{\equiv}7 (mod12) and p=n^2{\mp}n+1.<br />Comment: 8 pages
- Subjects :
- Mathematics - Number Theory
11G20, 14H25, 14K15, 14G99
Subjects
Details
- Database :
- arXiv
- Journal :
- Miskolc Mathematical Notes, Vol. 10 (2009), No. 2, 129-136
- Publication Type :
- Report
- Accession number :
- edsarx.1106.5851
- Document Type :
- Working Paper