manYPoints – Table of Curves with Many Points
Entry details for q = 72 = 49, g = 3
Table About Recent changes References
Username
Password
Log in Register

Lower bound Nmin = 92

Submitted by C. Ritzenthaler
Date 06-01-2009
Reference Jaap Top
Curves of genus 3 over small finite fields
Indag. Math. (N.S.) 14 (2003), no. 2, 275–283
Comments
This number of points in reached by the Fermat curve C: x^4+y^4+z^4=0.

Its Jacobian is isogenous to E^3 with trace(E)=-14. Its automorphism group (over F_q and geometric) has order 96.
Tags Explicit curves

User comments

Another example     
Everett Howe
05-20-2010 23:45
This number of points is also reached by the hyperelliptic curve y^2 = x^7 - x, which is the reduction of the Klein quartic in characteristic 7. Its automorphism group is the direct product of PGL(2,F_7) with the group of order 2 containing the hyperelliptic involution, so the automorphism group has order 672.
Upper bound Nmax = 92

Submitted by C. Ritzenthaler
Date 06-01-2009
Reference Not available
Comments
Tags None

User comments

No comments have been made.