  We consider the genus-one curves which arise in the cuts of the sunrise and
in the elliptic double-box Feynman integrals. We compute and compare invariants
of these curves in a number of ways, including Feynman parametrization,
lightcone and Baikov (in full and loop-by-loop variants). We find that the same
geometry for the genus-one curves arises in all cases, which lends support to
the idea that there exists an invariant notion of genus-one geometry,
independent on the way it is computed. We further indicate how to interpret
some previous results which found that these curves are related by isogenies
instead.
