Organic farming is a key element in achieving more sustainable agriculture. For a better understanding of the development and impact of organic farming, comprehensive, spatially explicit information is needed. This study presents an approach for the discrimination of organic and conventional farming systems using intra-annual Sentinel-2 time series. In addition, it examines two factors influencing this discrimination: the joint learning of crop type information in a concurrent task and the role of spatial context. A Vision Transformer model based on the Temporo-Spatial Vision Transformer (TSViT) architecture was used to construct a classification model for the two farming systems. The model was extended for simultaneous learning of the crop type, creating a multitask learning setting. By varying the patch size presented to the model, we tested the influence of spatial context on the classification accuracy of both tasks. We show that discrimination between organic and conventional farming systems using multispectral remote sensing data is feasible. However, classification performance varies substantially across crop types. For several crops, such as winter rye, winter wheat, and winter oat, F1 scores of 0.8 or higher can be achieved. In contrast, other agricultural land use classes, such as permanent grassland, orchards, grapevines, and hops, cannot be reliably distinguished, with F1 scores for the organic management class of 0.4 or lower. Joint learning of farming system and crop type provides only limited additional benefits over single-task learning. In contrast, incorporating wider spatial context improves the performance of both farming system and crop type classification. Overall, we demonstrate that a classification of agricultural farming systems is possible in a diverse agricultural region using multispectral remote sensing data.