manYPoints

Submitted by	C. Ritzenthaler
Date	06-01-2009
Reference	Jaap Top Curves of genus 3 over small finite fields Indag. Math. (N.S.) 14 (2003), no. 2, 275–283
Comments	This number of points in reached by the Fermat curve C: x^4+y^4+z^4=0. Its Jacobian is isogenous to E^3 with trace(E)=-14. Its automorphism group (over F_q and geometric) has order 96.
Tags	Explicit curves

Another example	Everett Howe 05-20-2010 23:45
This number of points is also reached by the hyperelliptic curve y^2 = x^7 - x, which is the reduction of the Klein quartic in characteristic 7. Its automorphism group is the direct product of PGL(2,F_7) with the group of order 2 containing the hyperelliptic involution, so the automorphism group has order 672.

Submitted by	Everett Howe
Date	06-10-2010
Reference	Jean-Pierre Serre Sur le nombre de points rationnels d'une courbe algébrique sur un corps fini C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 397–402. (= Œuvres III, No. 128, 658–663).
Comments	The Hasse-Weil-Serre bound
Tags	Hasse-Weil-Serre bound

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