Entry details for q = 22 = 4, g = 10
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Lower bound Nmin = 27

Submitted by Gerrit Oomens
Date 01/01/1900
Reference G. van der Geer, M. van der Vlugt
How to construct curves over finite fields with many points
In: Arithmetic Geometry, (Cortona 1994), F. Catanese Ed., Cambridge Univ. Press, Cambridge, 1997, p. 169-189.
Comments
Tags Elliptic modular curves

User comments

Explicit Curve     
S.E.Fischer
12/19/2014 18:42
We can assume such a curve C as an extension E of degree 4 of a maximal curve F of genus 1 as follows:
F := y^3 + x^3 + 1 ;
E/F := z^4 + z + x*y .
Upper bound Nmax = 27

Submitted by Everett Howe
Date 04/14/2010
Reference E. W. Howe and K. E. Lauter
Improved upper bounds for the number of points on curves over finite fields
Ann. Inst. Fourier (Grenoble) 53 (2003) 1677–1737.
Comments
A real Weil polynomial we don't know how to eliminate: (x + 2)^5 * (x + 4)^2 * (x^3 + 4*x^2 - x - 6)
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