Isogenies of Oriented Elliptic Curves

We construct and describe the moduli stack $\mathrm{Isog}$ of isogenies between oriented elliptic curves. We show that $\mathrm{Isog}$ is a spectral Deligne-Mumford stack and a relative spectral algebraic space over $\mathcal{M}_{\mathrm{ell}}^{\mathrm{or}}$, and give a fiber product decomposition o