Cardiovascular diseases (CVDs) are the most common health threats worldwide. 2D X-ray invasive coronary angiography (ICA) remains the most widely adopted imaging modality for CVD assessment during real-time cardiac interventions. However, it is often difficult for the cardiologists to interpret the 3D geometry of coronary vessels based on 2D planes. Moreover, due to the radiation limit, often only two angiographic projections are acquired, providing limited information of the vessel geometry and necessitating 3D coronary tree reconstruction based only on two ICA projections. In this paper, we propose a self-supervised deep learning method called NeCA, which is based on neural implicit representation using the multiresolution hash encoder and differentiable cone-beam forward projector layer, in order to achieve 3D coronary artery tree reconstruction from two 2D projections. We validate our method using six different metrics on a dataset generated from coronary computed tomography angiography of right coronary artery and left anterior descending artery. The evaluation results demonstrate that our NeCA method, without requiring 3D ground truth for supervision or large datasets for training, achieves promising performance in both vessel topology and branch-connectivity preservation compared to the supervised deep learning model.