Entry details for q = 21 = 2, g = 13
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Lower bound Nmin = 15

 Submitted by Gerrit Oomens Date 01/01/1900 Reference J-P. SerreLetter to G. van der GeerSeptember 1, 1997. Comments Tags Methods from general class field theory

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 Explicit Curve S.E.Fischer 12/19/2014 23:31 We can assume such a curve C as an extension E of degree 2 of a curve F of genus 4 as follows: F := y^4 + (x+1)*y^2 + (x^3+x)*y +x^7+x^3 ; E/F := z^2 + z + x*y . Defining equation Isabel Pirsic 06/18/2012 13:02 y^8 + (x^3 + x^2 + 1)*y^4 + (x^6 + x^4 + x^3 + x^2)*y^2 + (x^6 + x^4)*y + x^11 + x^7
Upper bound Nmax = 15

 Submitted by Everett Howe Date 04/14/2010 Reference Jean-Pierre SerreRational points on curves over finite fieldsNotes by Fernando Q. Gouvêa of lectures at Harvard University, 1985. Comments The Oesterlé bound. Here is a real Weil polynomial that we don't know how to eliminate: (x + 2) * (x^2 + x - 1) * (x^3 + 4*x^2 + 3*x - 1) * (x^7 + 5*x^6 - 28*x^4 - 20*x^3 + 35*x^2 + 14*x - 13) Tags Oesterlé bound

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