manYPoints – Table of Curves with Many Points
Entry details for q =
23
1
= 23
, g =
3
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Lower bound
N
min
= 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.
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Explicit curves
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Upper bound
N
max
= 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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