As noted in LMFDB/lmfdb#1403, we need to document and keep track of the indexes we are using, this has a big impact on the performance of the LMFDB, and lmfdb-inventory seems like the right place to do this. As an example/template, I have added index information to
https://github.com/LMFDB/lmfdb-inventory/blob/master/db-sato_tate_groups.md
(scroll down to the bottom to see the indexes).