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math.NT2002
Some genus 3 curves with many points
Roland Auer, Jaap Top
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…
math.NT2001
Legendre elliptic curves over finite fields
Roland Auer, Jaap Top
We show that every elliptic curve over a finite field of odd characteristic whose number of rational points is divisible by 4 is isogenous to an elliptic curve in Legendre form, wi…