The 1863-L cent. These are the famous issues with Longacre's initial 'L' on the ribbon.
These are actually restrikes using a reverse die from 1871 per Richard Snow. These restrikes are related to the 1863 two cent, trime, half dime and dime restrikes which were offered with the quarter, half dollar and dollar which were struck with the motto "In God We Trust" on the reverse.
Examples were struck as follows:
Bronze J301/P363 with about a half dozen known. The Connecticut State Library has at least one and possibly 2 if the oroide example noted below is actually another.
Copper nickel J302/P365 with about a half dozen known.
Oroide J303/P366 This is unconfirmed. The Mitchelson example in the Connecticut State Library appeared to me to be a second bronze piece.
Aluminum J304/P367 Only 2 are believed to exist including the illustrated example. One of these appeared in Elder's 38th March 1910 sale.
Photo courtesy of Richard Snow.