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. With contributions by Everett Howe, Joseph Oesterlé and Christophe Ritzenthaler. Edited by Alp Bassa, Elisa Lorenzo García, Christophe Ritzenthaler and René Schoof
Documents Mathématiques 18, Société Mathématique de France, Paris, 2020
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. With contributions by Everett Howe, Joseph Oesterlé and Christophe Ritzenthaler. Edited by Alp Bassa, Elisa Lorenzo García, Christophe Ritzenthaler and René Schoof
Documents Mathématiques 18, Société Mathématique de France, Paris, 2020
Comments
This upper bound is worked out on pages Se 68–69 of Serre's Harvard notes.
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None
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