This image above for the eagle used on J80/P87 was produced via a reducing lathe on a brass disk. It was not struck from a die.
It is illustrated as figure 81 on page 40 of the "History of the National Numismatic Collections" by Vladimir Clain-Stefanelli where it is described as a "Mechanical Reduction from cast bronze model to actual size used on pattern half dollar, 1838".
The cast bronze model used to produce it is also displayed as figure 80.
2 other mechanical reductions like this on brass square planchets are also known, one ex Mint Director Patterson's estate and the other ex Heritage 8/2015 ANA.
Image courtesy of the National Numismatic Collection of the Smithsonian Institution.