Submitted by 
Gerrit Oomens 
Date 
01011900 
Reference 
Gerard van der Geer, Marcel 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. 169189.

Comments


Tags 
Elliptic modular curves 
User comments
Explicit Curve

S.E.Fischer
02242017 21:47

Another equation is given by
(x^4 + 1)*y^4 + 2*x^3*y^3 + y^2 + 2*x*y + x^4 + x^2 = 0.

Other reference

C. Ritzenthaler
02012013 10:01

A curve is also constructed in the paper "polynomials with a restricted range and curves with many points" by C.A. Ramos and A.G. Ramos. Let a be a root of x^2+x+2=0. Then
y^8=a^2 x^2 (x^2+a^7)
has 32 points over F_9.


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