Digitalization appears as a lever to enhance agriculture sustainability. However, existing works on digital agriculture's own sustainability remain scarce, disregarding the environmental effects of deploying digital devices on a large-scale. We propose a bottom-up method to estimate the carbon footprint of digital agriculture scenarios considering deployment of devices over a diversity of farm sizes. It is applied to two use-cases and demonstrates that digital agriculture encompasses a diversity of devices with heterogeneous carbon footprints and that more complex devices yield higher footprints not always compensated by better performances or scaling gains. By emphasizing the necessity of considering the multiplicity of devices, and the territorial distribution of farm sizes when modelling digital agriculture deployments, this study highlights the need for further exploration of the first-order effects of digital technologies in agriculture.