File talk:Coa Conti di Segni.svg
This coa is all over the place because it is "papal". But it was used by three popes, two in the 13th century and one in the 18th. This makes research difficult. It isn't even certain that the first of these popes even used it, it may just have been attributed to him because he was of the same family as the later two. That first pope would have been Innocent III, elected 1198. It is uncertain that he even continued to use his family coa as pope, if he did, he would be the first known pope to do so. We know the popes began doing this by the 1240s, and the second Conti pope, Alexander IV, was elected in 1254, so he probably did. I am still not aware that there is a contemporary reference confirming he did, but it stands to reason.
Now the third Conti pope was Innocent XIII, elected 1721, very much in the "age of heraldry", so it should be easy to verify if he used a crowned eagle or not. In fact, here is one of his coins. But the early heraldic sources showing the papal coas predate 1721, and there are plenty of 17th-century depictions of the 13th-century popes' coa showing a crowned eagle. Apparently the Vatican does not now show these eagles crowned, so more research is needed.
Here is an 1882 source stating with no further ado that the eagle of all three Conti popes was crowned or. But here we find "In the 14th century and after, the eagle is usually found crowned." So this would seem to explain it, the crownless image should be used to depict the historical coa of the 13th century popes, but a crowned eagle was often attributed to them, and it is open to question whether Innocent III even did have "historical" arms, so that showing his reconstructed arms would be even more of an anachronism than just showing the arms attributed to him in classical heraldry.
Here we see that the crown is not attached to the eagle's head, but hovering above it, so it might also be described as in chief a ducal coronet or (here, but in this source, the eagle is also checquée argent and sable instead of or and sable).
