Entry details for q = 711 = 71, g = 3
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Lower bound Nmin = 120

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=36. 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)=-16 and the automorphism group of C is S_4.
Tags Explicit curves

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Upper bound Nmax = 120

Submitted by C. Ritzenthaler
Date 06/01/2009
Reference Not available
Comments
Tags None

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