Accurate segmentation of the aorta and its branches is essential for the diagnosis and treatment planning of vascular diseases. In this work, we propose a two-stage deep learning framework specifically designed for multi-class segmentation of the aorta and its primary branches. The first stage employs a self-supervised 3D Student-Teacher Learning Framework to pretrain the encoder on unlabeled medical images, enabling the model to learn rich anatomical representations without manual annotations. In the second stage, we fine-tune an xLSTM-based UNet architecture using the labeled training set from the AortaSeg24 Challenge, which consists of 50 annotated 3D computed tomography angiography (CTA) scans. The model is validated on 10 cases and evaluated on a hidden test set of 40 cases. Our method achieves an overall Dice score of \(0.737\pm 0.08\) on the test set, better than both the baseline xLSTM and the widely adopted nnUNet. The integration of xLSTM modules effectively captures both long-range dependencies and local spatial details, improving segmentation accuracy in complex vascular anatomies. This framework demonstrates robustness in anatomically challenging regions and efficient utilization of limited labeled data through self-supervised learning. Our findings highlight the clinical potential of combining self-supervised pretraining with advanced recurrent architectures to deliver scalable, reliable segmentation tools that support more accurate and informed vascular interventions.