Minimisation and reduction of 5-coverings of elliptic curves. (English) Zbl 1300.11058

Fisher, Tom

Algebra Number Theory 7, No. 5, 1179-1205 (2013).

Summary: We consider models for genus-1 curves of degree 5, which arise in explicit 5-descent on elliptic curves. We prove a theorem on the existence of minimal models with the same invariants as the minimal model of the Jacobian elliptic curve and give an algorithm for computing such models. Finally we describe how to reduce genus-1 models of degree 5 defined over \(\mathbb Q\).

MSC:

11G05	Elliptic curves over global fields
11G07	Elliptic curves over local fields
14H52	Elliptic curves
14H25	Arithmetic ground fields for curves

Keywords:

elliptic curves; genus-1 curves; minimisation; reduction; descent

Software:

Magma