I use the firmware download website as my definitive reference for which firmware will work in which hardware.
The 1769-L2x series controllers are supported only by RSLogix 5000 version 17 and higher.
The 1769-L3x series controllers have been supported since their initial releases. The -L35E was released as a v12 controller, and the -L31, -L32E, L32C, and -L35CR were released as v13 controllers.
All 1769-L3x CompactLogix controllers will therefore support v16 firmware, while all 1769-L2x controllers require v17.