3 citations · 5 across the 4 of their papers we have counts for
8 papers
Arithmetic of the [19,1,1,1,1,1] fibration
Matthias Schuett, Jaap Top
This paper studies the arithmetic of the extremal elliptic K3 surface with configuration of singular fibres [19,1,1,1,1,1]. We give a model over Q such that the Neron Severi group…
An isogeny of K3 surfaces
Bert van Geemen, Jaap Top
In a recent paper Ahlgren, Ono and Penniston described the L-series of K3 surfaces from a certain one parameter family in terms of those of a particular family of elliptic curves.…
Explicit equations of some elliptic modular surfaces
Jaap Top, Noriko Yui
We present explicit equations of semi-stable elliptic surfaces (i.e., having only type singular fibers) which are associated to the torsion-free genus zero congruence subgrou…
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…