Maximality of Ciani curves over finite fields |
| |
Affiliation: | 1. Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People''s Republic of Korea;2. PGItech Corp., Pyongyang, Democratic People''s Republic of Korea;3. Department of Mathematics, University of Paris VIII, F-93526 Saint-Denis, France;4. University Sorbonne Paris Cité, LAGA, UMR 7539, CNRS, 93430 Villetaneuse, France;5. Telecom Paris, Polytechnic Institute of Paris, 91120 Palaiseau, France;1. Sabanc? University, Istanbul, Turkey;2. University of Auckland, Auckland, New Zealand;1. Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China;2. School of Mathematical Sciences, Anhui University, Hefei, 230601, China;3. Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey;4. I2M, Aix Marseille Univ., Centrale Marseille, CNRS, Marseille, France |
| |
Abstract: | In this paper, we will study Ciani curves in characteristic , in particular their standard forms . It is well-known that any Ciani curve is a non-hyperelliptic curve of genus 3, and its Jacobian variety is isogenous to the product of three elliptic curves. As a main result, we will show that if C is superspecial, then belong to and C is maximal or minimal over . Moreover, in this case we will provide a simple criterion in terms of that tells whether C is maximal (resp. minimal) over . |
| |
Keywords: | Algebraic curve Curve of genus 3 Superspecial curve Maximal curve |
本文献已被 ScienceDirect 等数据库收录! |
|