The purpose of this paper is to present two theorems which give an overview of the set of elliptic curves lying on an abelian surface and to discuss several applications. One of these applications isâ€¦ (More)

Let E be an elliptic curve over a field K of characteristic 6= 2 and let N > 1 be an integer prime to char(K). The purpose of this paper is to study the family of genus 2 covers of E of fixed degreeâ€¦ (More)

Let X be a smooth projective curve over C which admits a finite group G of automorphisms. Then GÃ—G acts on the product surface Y = X Ã—X, and so for each subgroup H â‰¤ GÃ—G, the quotient Z = H\Y is aâ€¦ (More)

Let C be a curve of genus 2 defined over an algebraically closed field K, and suppose that C admits a non-constant morphism f : C â†’ E to an elliptic curve E. If f does not factor over an isogeny ofâ€¦ (More)

where Î g(C) is the geometric (profinite) fundamental group of CÃ—Spec(Ks) (i.e. Î g(C) is equal to the Galois group of the maximal unramified extension of F (C)âŠ—Ks). This sequence induces aâ€¦ (More)

of the maximal unramified extension Fnr,P of F in which P splits completely. Since the extension Fnr,P/F is regular, it is clear that Ï€1(C,P ) is a quotient of the usual geometric fundamental groupâ€¦ (More)

The purpose of this article is to give a partly historical survey of the main results on Eulerâ€™s idoneal numbers and to study several generalizations. Some of these generalizations were suggested byâ€¦ (More)

The present variant is almost identical with the one from 1990. The main change is a correction in proof of Lemma 2.4, which was pointed out to me by Matthias Flach. I would also like to give myâ€¦ (More)

The main aim of this paper is to determine the number cN,D of genus 2 covers of an elliptic curve E of fixed degree N â‰¥ 1 and fixed discriminant divisor D âˆˆ Div(E). In the case that D is reduced,â€¦ (More)