Deep learning-based image compression has made great progresses recently. However, many leading schemes use serial context-adaptive entropy model to improve the ratedistortion (R-D) performance, which is very slow. In addition, the complexities of the encoding and decoding networks are quite high and not suitable for many practical applications. In this paper, we introduce four techniques to balance the tradeoff between the complexity and performance. We are the first to introduce deformable convolutional module in compression framework, which can remove more redundancies in the input image, thereby enhancing compression performance. Second, we design an improved checkerboard context model with two separate distribution parameter estimation networks and different probability models, which enables parallel decoding without sacrificing the performance compared to the sequential contextadaptive model. Third, we develop a three-step knowledge distillation and training scheme to achieve different trade-offs between the complexity and the performance of the decoder network, which transfers both the final and intermediate results of the teacher network to the student network to help its training. Fourth, we introduce L1 regularization to make the numerical values of the latent representation more sparse. Then we only encode non-zero channels in the encoding and decoding process, which can greatly reduce the encoding and decoding time. Experiments show that compared to the state-of-the-art learned image coding scheme, our method can be about 20 times faster in encoding and 70-90 times faster in decoding, and our R-D performance is also 2.3% higher. Our method outperforms the traditional approach in H.266/VVC-intra (4:4:4) and some leading learned schemes in terms of PSNR and MS-SSIM metrics when testing on Kodak and Tecnick-40 datasets.