manYPoints – Table of Curves with Many Points
Entry details for q = 114 = 14641, g = 3
Table About Recent changes References
Username
Password
Log in Register

Lower bound Nmin = 15368

Submitted by C. Ritzenthaler
Date 11-15-2009
Reference Tomoyoshi Ibukiyama
On rational points of curves of genus 3 over finite fields
Tohoku Math. J. (2) 45 (1993) 311–329
Comments
This number is reached by a supersingular hyperelliptic curve of genus 3. This is proved using the class number formula of ternary quaternion Hermitian forms by Hashimoto.
Tags None

User comments

Explicit example     
Everett Howe
05-20-2010 23:50
One such hyperelliptic curve is n*y^2 = x^7 + 5*x^5 + 5*x^3 + x, where n is any element of F_{11^4} that is not a square.
Upper bound Nmax = 15368

Submitted by C. Ritzenthaler
Date 11-15-2009
Reference Not available
Comments
Tags None

User comments

No comments have been made.