Elliptic subcovers of a curve of Genus 2 II. The refined Humbert invariant

Let C/K be a curve of genus 2 over an arbitrary field K. The first part of this two-part paper established a bijection between the set of equivalence classes of the elliptic subcovers of C/K and the set of certain primitive representations of an intrinsic quadratic form qC called the refined Humbert invariant. This second part explains how to compute the refined Humbert invariant explicitly from a presentation of the Jacobian variety JC of C.