manYPoints – Table of Curves with Many Points
Entry details for q = 21 = 2, g = 23
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Lower bound Nmin = 22

Submitted by Gerrit Oomens
Date 01-01-1900
Reference Chaoping Xing, Harald Niederreiter
Drinfeld modules of rank 1 and algebraic curves with many rational points
Monatsh. Math. 127 (1999) 219–241
Comments
Tags Methods from general class field theory

User comments

Explicit equation     
Isabel Pirsic
04-25-2013 17:04
This one took magma more than 40 days ...

y^22 +
x*y^20 +
(x^3 + x^2 + x)*y^19 +
(x^8 + x^7 + x^3 + x^2 + 1)*y^18 +
(x^7 + x^6 + x^5 + x^3 + x^2 + x)*y^17 +
(x^11 + x^5 + x^2 + x)*y^16 +
(x^9 + x^8 + x^6)*y^15 +
(x^16 + x^13 + x^11 + x^10 + x^8 + x^7 + x^6 + x^4 + x^2 + 1)*y^14 +
(x^11 + x^10 + x^8 + x^7 + x^6 + x^5)*y^13 +
(x^17 + x^14 + x^13 + x^12 + x^11 + x^9 + x^7 + x^6 + x^3 + x)*y^12 +
(x^19 + x^18 + x^17 + x^14 + x^13 + x^11 + x^10 + x^9 + x^7 + x^5 + x^4 + x^2 + x)*y^11 +
(x^24 + x^23 + x^12 + x^11 + x^8 + x^5 + x^3 + x^2 + 1)*y^10 +
(x^23 + x^22 + x^21 + x^19 + x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^6 + x^4 + x^2 + x)*y^9 +
(x^27 + x^23 + x^22 + x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^2 + x)*y^8 +
(x^25 + x^24 + x^20 + x^18 + x^17 + x^15 + x^14 + x^11 + x^10 + x^9 + x^4 + x^3)*y^7 +
(x^29 + x^25 + x^24 + x^23 + x^17 + x^15 + x^14 + x^11 + x^10 + x^6 + x^4 + x^2)*y^6 +
(x^27 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^12 + x^7 + x^6 + x^4 + x^3)*y^5 +
(x^31 + x^28 + x^27 + x^26 + x^23 + x^21 + x^20 + x^19 + x^18 + x^15 + x^14 + x^13 + x^10 + x^8 + x^6 + x^5 + x^3)*y^4 +
(x^29 + x^28 + x^27 + x^24 + x^23 + x^21 + x^20 + x^18 + x^14 + x^13 + x^12 + x^10 + x^9 + x^7 + x^6 + x^5)* y^3 +
(x^33 + x^32 + x^30 + x^25 + x^24 + x^23 + x^22 + x^19 + x^17 + x^14 + x^13 + x^12 + x^8 + x^7 + x^5)*y^2 +
(x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^20 + x^19 + x^16 + x^15 + x^14 + x^13 + x^9 + x^8 + x^7)* y +
x^33 + x^31 + x^30 + x^28 + x^27 + x^25 + x^24 + x^22 + x^21 + x^15 + x^14 + x^13 + x^11 + x^10 + x^8
Upper bound Nmax = 23

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
Tags Oesterlé bound

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