153 research outputs found
Curves of genus 3 over small finite fields
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 quartics over finite fields are given.Comment: 9 page
A singular K3 surface related to sums of consecutive cubes
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 properties in detail. We construct
elliptic fibrations on it, and we find a parametric solution to the original
equation. Also, we determine the Hasse-Weil zeta function of the surface over
Legendre elliptic curves over finite fields
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, with the sole exception of a minimal respectively
maximal elliptic curve. We also collect some results concerning the
supersingular Legendre parameters
Twists of Elliptic Curves
In this note we extend the theory of twists of elliptic curves as presented
in various standard texts for characteristic not equal to two or three to the
remaining characteristics. For this, we make explicit use of the correspondence
between the twists and the Galois cohomology set
. The results are illustrated by
examples
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