Some genus 3 curves with many points
Roland Auer, Jaap Top
Abstract
Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We also provide an intrinsic characterization of so-called Legendre elliptic curves.
Create a lesson
Related papers
Unit fraction representations using shifted Golomb primes
Rishika Agrawal
Improved deterministic integer factorization by quadratic-image sieving
Pantelimon Stănică
Private key sieves for improved attacks on RSA
Markus Hittmeir
Multiple q-zeta values as polynomials in partition multiplicities
Jan-Willem M. van Ittersum
Hopf-Galois Structures on Extensions Arising from Division Points on Elliptic Curves
Leolin Nkuete
Certified Collision Exclusion and an Unconditional Upper Bound Λ<0.156821 for the de Bruijn--Newman Constant
Michel Planat, Dale James Raymond