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 C. P. Xing, H. Niederreiter
Drinfeld modules of rank 1 and algebraic curves with many rational points
Monatsh. Math. 127 (1999), p. 219-241.
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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 Gerrit Oomens
Date 01/01/1900
Reference C. P. Xing, H. Niederreiter
Drinfeld modules of rank 1 and algebraic curves with many rational points
Monatsh. Math. 127 (1999), p. 219-241.
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