Curtis will be more certain of
his answer than I am, but I am reasonably confident that the initials, standing alone, can either be read taking 'ex' for granted or as an ablative absolute, usually translated somewhat awkwardly (English lacking an absolute construction, though I just came as close as possible to making one) as 'the Senate having decreed' or 'by decree of the Senate'. All ablatives are adverbial in nature: when, where, how.
I don't think that a nominative would stand naked on a coin except as a label, and even that is the exception. That is why persons who didn't take Latin in school are prone to talking about 'the Genio' (which is actually a dative): one seldom sees 'Genius' on a coin.
Of course, they didn't have to issue a fresh decree for each issue, so it doesn't matter if we want to think of S C as simply marking senatorial coinage.
Pat L.