In the book Monuments of Ancient Rome as Coin Type by P V Hill he speculates that the accusative case, rarely used for coin reverses, suggests that in those instances the reference is to a statue. A note in Zapiski Numizmatyczne XV, 2020, explores that hypothesis.
Taking the examples of the CEREREM and IVNONEM reverses of Julia Domna as a case in point the paper examines wider literary and epigraphical conventions. It concluded that a verb, perhaps posuit (erected), consecravit (consecrated) or dedicavit (dedicated) is unwritten on the coin reverses, but would have been understood, when combined with the accusative. This, the above sestertius of Domna has a representation on the reverse of a statue to Juno, accompanied by a small peacock, although it has been noted that there are versions with the peacock's head to both the left and the right.
The MARTEM PROPVGNATOREM reverse of Gordian III from his 5th Rome emission (c.243-4 AD) is a further example cited and should be interpreted as Gordian dedicating (etc.) a statue of Mars the defender. The timing of this issue is interesting. It may be associated with the campaign of Gordian in the East that set off in 243 to counter the army of the Sasanid ruler Shapur I. Before setting out on it is documented that Gordian arranged for the doors of the Temple of Janus in Rome to be opened, indicating that the state was at war and, according to legend, when opened the doors of the Temple let forth a deluge of water to protect the citizens from attackers in a last desperate measure. The invocation of Mars the defender, with the dedication of a new statue or shrine at this time, would be appropriate.
Link to the paper:
