Minimisation and reduction of 5-coverings of elliptic curves

Details Minimisation and reduction of 5-coverings of elliptic curves Minimisation and reduction of 5-coverings of elliptic curves

2011-12-21

arxiv.org/abs/1112.5131v1

Mathematics

Number Theory

27 pages

Scientific paper

We consider models for genus one 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 one models of degree 5 defined over Q.

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