Learned image compression (LIC) has recently benefited from Transformer- and state space models (SSM)- based backbones for modeling long-range dependencies. However, the former typically incurs quadratic complexity, whereas the latter often disrupts neighborhood continuity by flattening 2D features into 1D sequences. To address these issues, we propose a compact Hybrid Convolution and Frequency State Space Network (HCFSSNet) for LIC. HCFSSNet combines convolutional layers for local detail modeling with a Vision Frequency State Space (VFSS) block for complementary long-range contextual aggregation. Specifically, the VFSS block consists of a Vision Omni-directional Neighborhood State Space (VONSS) module, which scans features along horizontal, vertical, and diagonal directions to better preserve 2D neighborhood relations, and an Adaptive Frequency Modulation Module (AFMM), which performs discrete cosine transform-based adaptive reweighting of frequency components. In addition, we introduce a Frequency Swin Transformer Attention Module (FSTAM) in the hyperprior path to enhance frequency-aware side information modeling. Experiments on the benchmark datasets show that the proposed HCFSSNet achieves a competitive rate-distortion performance against recent LIC codecs. The source code and models will be made publicly available.