This variety is in a section for which the collection records show planting dates of 1998, 2005 or nothing. This variety has no planting date or source listed.
The register entry is:
Cardinal. (C.japonica), Hovey, 1838, Magazine of Horticulture. Bright red, full peony. Originated in the USA.
Clearly, this description is a poor match for the pink formal double flowers on the collection specimen. There are probably quite a few contenders for the identity of this one, even in the collection there are a number that look very similar. It is also likely to be a very old variety, reducing the chances of accurate identification still further.
Leaves 10-11cm long including 1cm petiole, 4.5-5.8cm wide. Flowers around 8cm wide.