An Explicit Theory of Heights
E. V. Flynn · Transactions of the American Mathematical Society · 1995
We consider the problem of explicitly determining the naive height constants for Jacobians of hyperelliptic curves. For genus $> 1$, it is impractical to apply Hilbert’s Nullstellensatz directly to the defining equations of the duplication law; we indicate how this technical difficulty can be overcome by use of isogenies. The height constants are computed in detail for the Jacobian of an arbitrary curve of genus $2$, and we apply the technique to compute generators of $\mathcal {J}(\mathbb {Q})$, the Mordell-Weil group for a selection of rank $1$ examples.