manYPoints – Table of Curves with Many Points
Entry details for q = 72 = 49, g = 4
Table About Recent changes References
Username
Password
Log in Register

Lower bound Nmin = 102

Submitted by Everett Howe
Date 02-16-2014
Reference Everett W. Howe
Quickly constructing curves of genus 4 with many points
Frobenius Distributions: Sato–Tate and Lang–Trotter conjectures (D. Kohel and I. Shparlinski, eds.), Contemporary Mathematics 663, American Mathematical Society, Providence, RI, 2016, pp. 149–173
Comments
Explicit curve: y^2 = x^3 + 3*x, z^2 = x^3 + x^2 + 6*x + 1.
Tags Explicit curves

User comments

Explicit Curve     
S.E.Fischer
02-24-2017 20:56
Another equation is given by
x^3*y^3 + x^6 + y^6 + 5*x^2*y^2 + x*y + 6 = 0.
Upper bound Nmax = 102

Submitted by Everett Howe
Date 07-16-2016
Reference Momonari Kudo, Shushi Harashita
Superspecial curves of genus $4$ in small characteristic
Finite Fields Appl. 45 (2017), 131–169
Comments
Theorem B of the cited reference shows that defect 0 is impossible. Then other methods show that defects 1, 2, and 3 are also impossible — for example, the Magma programs in IsogenyClasses.magma (http://alumnus.caltech.edu/~however/papers/paper35.html) can prove this.
Tags Analysis and enumeration

User comments

No comments have been made.