We consider models for genus-one curves of degree n for n= 2, 3 and 4, which arise in
explicit n-descent on elliptic curves. We prove theorems on the existence of minimal models …

Trace Zero Points on Elliptic Fibrations Page 1 University of California Santa Barbara Trace
Zero Points on Elliptic Fibrations A dissertation submitted in partial satisfaction of the …

Let C be a soluble smooth genus one curve over a Henselian discrete valuation field. There
is a unique minimal Weierstrass equation defining C up to isomorphism. In this paper we …

In this paper we consider genus one equations of degree $ n $, namely a (generalised)
binary quartic when $ n= 2$, a ternary cubic when $ n= 3$, and a pair of quaternary quadrics …

We study genus one curves that arise as $2 $-, $3 $-and $4 $-coverings of elliptic curves.
We describe efficient algorithms for testing local solubility and modify the classical formulae …

Let E be an elliptic curve defined over a number field K. An n-descent on E computes the n-
Selmer group Sel(n)(K, E) of E, which parametrises the everywhere locally soluble n …

In dieser Arbeit beschäftigen wir uns mit der Berechnung von Mordell-Weil-Basen für eine
elliptische Kurve A über einem globalen Funktionenkörper K. Insbesondere interessiert uns …

Die Arbeit beschäftigt sich mit der Berechnung von Mordell-Weil-Basen für elliptische
Kurven A über einem globalen Funktionenkörper K. Besonderes Interesse gilt dem Fall char …

Let E be an elliptic curve defined over a number field K. An n-covering of E is a principal
homogeneous space C for E together with a map π: C→ E which can be factored as π≃[n]◦ …