The monitoring and surveillance of maritime activities are critical issues in both military and civilian fields, including among others fisheries monitoring, maritime traffic surveillance, coastal and at-sea safety operations, tactical situations. In operational contexts, ship detection and identification is traditionally performed by a human observer who identifies all kinds of ships from a visual analysis of remotely-sensed images. Such a task is very time consuming and cannot be conducted at a very large scale, while Sentinel-1 SAR data now provide a regular and worldwide coverage. Meanwhile, with the emergence of GPUs, deep learning methods are now established as state-of-the-art solutions for computer vision, replacing human intervention in many contexts. They have been shown to be adapted for ship detection, most often with very high resolution SAR or optical imagery. In this paper, we go one step further and investigate a deep neural network for the joint classification and characterization of ships from SAR Sentinel-1 data. We benefit from the synergies between AIS (Automatic Identification System) and Sentinel-1 data to build significant training datasets. We design 12 a multi-task neural network architecture composed of one joint convolutional network connected to three task-specific networks, namely for ship detection, classification and length estimation. The experimental assessment showed our network provides promising results, with accurate classification and length performance (classification overall accuracy: 97.25%, mean length error: 4.65 m ± 8.55 m).