Database download information
The LinkInfo database has two parts, the collection of link invariants and the collection of diagrams. Both can be downloaded in full. However, BE WARNED both databases are very large.
LinkInfo invariants are kept in an Excel Spreadsheet. For each invariant, there are two columns: one has the value of the invariant, the other has possible links to references. It should not be hard to isolate out the data of interest. The file is roughly 11MB: Database of link invariants.
The diagrams in LinkInfo are png and svg files. The full collection can be downloaded as two separate compressed files, each roughly 40MB. Unpacked they contain about 9,000 files: for each link there is a diagram of the link, its mirror image, and a thumbnail sketch. The download is: Link Diagrams - Knotscape.