Depending on the download type, you should use either or both of the following two options:
aria2c --continue=true \
But, you will apparently need the url for the download with both options. As far as I can tell, you cannot resume a download without it. I'm sorry this couldn't be better help, but the docs are here. These options are described thus:
Downloads URIs found in FILE. You can specify multiple URIs for a single entity: separate URIs on a single line using the TAB character. Reads input from stdin when - is specified. Additionally, options can be specified after each line of URI. This optional line must start with one or more white spaces and have one option per single line. The input file can use gzip compression. See Input File subsection for details. See also
Continue downloading a partially downloaded file. Use this option to resume a download started by a web browser or another program which downloads files sequentially from the beginning. Currently this option is only applicable to HTTP(S)/FTP downloads.