Recently, AI-generated content (AIGC) has gained significant traction due to its powerful creation capability. However, the storage and transmission of large amounts of high-quality AIGC images inevitably pose new challenges for recent file formats. To overcome this, we define a new file format for AIGC images, named AIGIF, enabling ultra-low bitrate coding of AIGC images. Unlike compressing AIGC images intuitively with pixel-wise space as existing file formats, AIGIF instead compresses the generation syntax. This raises a crucial question: Which generation syntax elements, e.g., text prompt, device configuration, etc, are necessary for compression/transmission? To answer this question, we systematically investigate the effects of three essential factors: platform, generative model, and data configuration. We experimentally find that a well-designed composable bitstream structure incorporating the above three factors can achieve an impressive compression ratio of even up to 1/10,000 while still ensuring high fidelity. We also introduce an expandable syntax in AIGIF to support the extension of the most advanced generation models to be developed in the future.