manYPoints – Table of Curves with Many Points
Entry details for q =
29
1
= 29
, g =
3
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Lower bound
N
min
= 60
Submitted by
C. Ritzenthaler
Date
06/01/2009
Reference
Jean-Pierre Serre
Rational points on curves over finite fields
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
Comments
This number of points is reached by the curve C: x^4+y^4+z^4+2*a*(x^2*y^2+y^2*z^2+z^2*x^2)=0 with a=13. This curve was found by M. Nitzberg (see loc. cit. p.72). See also Top : Curves of genus 3 over small finite fields.
Its Jacobian is isogenous to E^3 with trace(E)=-10 and the automorphism group of C is S_4.
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Upper bound
N
max
= 60
Later entry
Submitted by
C. Ritzenthaler
Date
06/01/2009
Reference
Not available
Comments
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None
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