manYPoints

Submitted by	Gerrit Oomens
Date	01-01-1900
Reference	Jean-Pierre Serre Letter to G. van der Geer September 1, 1997.
Comments
Tags	Methods from general class field theory

Correction	S.E.Fischer 12-20-2014 03:42
The extension E/F leads to a curve of genus 4 with 8 points. Extending once again by H of degree 2 leads to the desired result, as we write H/(E/F):= v^2 + v + x^3 + x .
Explicit Curve	S.E.Fischer 12-18-2014 15:30
We can assume such a curve C as an extension E of degree 2 of a curve F of genus 1 as follows: F: (x + y + xy) x*y + x + 1 ; E/F := v^2 + v + x^3 + x .
Defining equation	Isabel Pirsic 06-18-2012 13:00
(x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)y^8 + (x^10 + x^9 + x^6 + x^5 + x + 1)y^4 + (x^13 + x^12 + x^11 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2)y^2 + (x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^6 + x^5)y + x^21 + x^20 + x^17 + x^15 + x^11 + x^10 + x^8 + x^6

Submitted by	Everett Howe
Date	04-14-2010
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	The Oesterlé bound. Here is a real Weil polynomial that we don't know how to eliminate: (x^2 + 2x - 1) (x^3 + 4x^2 + 3x - 1) * (x^6 + 5x^5 + 3x^4 - 16x^3 - 18x^2 + 9*x + 11)
Tags	Oesterlé bound

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