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| Submitted by |
Gerrit Oomens |
| Date |
01-01-1900 |
| Reference |
Jean-Pierre Serre
Nombre de points des courbes algébriques sur F_q
Sém. de Théorie des Nombres de Bordeaux, 1982/83, exp. no. 22. (= Oeuvres III, No. 129, p. 664-668).
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Comments
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| Tags |
Explicit curves |
User comments
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Explicit Curve
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S.E.Fischer
12-26-2014 00:31
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We can assume such a curve C as an extension E of degree 3 of a curve F of genus 1 with eight rational points as follows:
F:= y^2 +y +x + 1/x ;
E/F := z^3*x^2 +y +1 .
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Explicit example
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Everett Howe
05-20-2010 21:51
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In his Harvard notes, Serre notes that a model of the Klein curve gives an example of a genus-3 curve with 14 points:
(x + y + z)^4 + (x*y + x*z + y*z)^2 + x*y*z*(x + y + z) = 0
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