3 citations · 5 across the 4 of their papers we have counts for
5 papers · 1 filter
Curves of genus 3 over small finite fields
Jaap Top
We present a table containing the maximal number of rational points on a genus 3 curve over a field of cardinality q, for all q<100. Also, some remarks on Frobenius non-classical q…
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…
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…
Sections on certain j=0 elliptic surfaces
Jasbir Chahal, Matthijs Meijer, Jaap Top
Using some theory of (rational) elliptic surfaces plus elementary properties of a Mordell-Weil group regarded as module over the endomorphism ring of a (CM) elliptic curve, we pres…
A singular K3 surface related to sums of consecutive cubes
Masato Kuwata, Jaap Top
We study the surface arising from the diophantine equation . It turns out that this is a surface with Picard number 20. We stduy its aritmetic p…