Entry details for q = 231 = 23, g = 3
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Lower bound Nmin = 48

Submitted by C. Ritzenthaler
Date 05/26/2009
Reference Jean-Pierre Serre
Rational points on curves over finite fields
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
Comments
This number of points is reached by the curve C : x^4+y^4+z^4-5*(x^2*y^2+x^2*z^2+y^2*z^2)=0. Its Weil polynomial is (X^2+8*X+23)^3. Its automorphism group is S_4.
Tags Explicit curves

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Upper bound Nmax = 48

Submitted by Everett Howe
Date 06/11/2010
Reference Jean-Pierre Serre
Rational points on curves over finite fields
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
Comments
This upper bound is worked out on pages Se 68–69 of Serre's Harvard notes.
Tags None

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