Epilepsy is a disease caused by abnormal neural discharge, which severely harms the health of patients. Its pathogenesis is complex and variable with various forms of seizures, leading to significant differences in epilepsy manifestations among different patients. The changes of brain network are strongly correlated with related pathologies. Therefore, it is crucial to effectively and deeply explore the intrinsic features of epilepsy signals to reveal the rules of epilepsy occurrence and achieve accurate detection. Existing methods have faced the following issues: 1) single approach for feature extraction, resulting in insufficient classification information due to the lack of rich dimensions in captured features; 2) inability to deeply analyze the essential commonality of epilepsy signal after feature extraction, making the model susceptible to data distribution and noise interference. Thus, we proposed a high-precision and robust model for epileptic seizure detection, which, for the first time, applies hypergraph convolution to the field of epilepsy detection. Through a hypergraph network structure constructed based on relationships between channels in electroencephalogram (EEG) signals, the model explores higher-order characteristics of epilepsy EEG data. Specifically, we use the Conv-LSTM module and Power spectral density (PSD), a two-branch parallel method, to extract channel features from space-time and frequency domains to solve the problem of insufficient feature extraction, and can adequately describe the data structure and distribution from multiple perspectives through double-branch parallel feature extraction. In addition, we construct a hypergraph on the captured features to explore the intrinsic features in the high-dimensional space in an attempt to reveal the essential commonality of epileptic signal feature extraction. Finally, using the ensemble learning concept, we accomplished epilepsy detection on the dual-branch hypergraph convolution. The model underwent leave-one-out cross-validation on the TUH dataset, achieving an average accuracy of 96.9%, F1 score of 97.3%, Pre of 98.2% and Re of 96.7%. In addition, the model was generalized performance tested on CHB-MIT scalp EEG dataset with leave-one-out cross-validation, and the average ACC, F1 score, Pre and Re were 94.4%, 95.1%, 95.8%, and 93.9% respectively. Experimental results indicate that the model outperforms related literature, providing valuable reference for the clinical application of epilepsy detection.