Cuts and isogenies

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