3 citations · 7 across the 6 of their papers we have counts for
6 papers
Index calculus with double large prime variation for curves of small genus with cyclic class group
Claus Diem
We present an index calculus algorithm with double large prime variation which lends itself well to a rigorous analysis. Using this algorithm we prove that for fixed genus $g \geq…
Ordinary elliptic curves of high rank over with constant j-invariant II
Claus Diem, Jasper Scholten
We show that for all odd primes , there exist ordinary elliptic curves over with arbitrarily high rank and constant -invariant. This shows in particul…
On the Structure of the Weil Restriction of Abelian Varieties
Claus Diem, N. Naumann
We give a description of endomorphism rings of Weil restrictions of abelian varieties with respect to finite Galois extensions. The results are applied to study the isogeny decompo…
Non-constant curves of genus 2 with infinite pro-Galois covers
Claus Diem, Gerhard Frey
For every odd prime number p, we give examples of non-constant smooth families of genus 2 curves over fields of characteristic p which have pro-Galois (pro-étale) covers of infinit…
Families of elliptic curves with genus 2 covers of degree 2
Claus Diem
We study genus 2 covers of relative elliptic curves over an arbitrary base in which 2 is invertible. Particular emphasis lies on the case that the covering degree is 2. We show tha…
Ordinary elliptic curves of high rank over with constant j-invariant
Irene I. Bouw, Claus Diem, Jasper Scholten
We show that under the assumption of Artin's Primitive Root Conjecture, for all primes p there exist ordinary elliptic curves over with arbitrary high rank and consta…