It's apparently the ablative. Found another example on Wiktionary using it: multō sanguine victōria nōbīs cōnstitit. (The victory cost us much blood.)
Allen and Greenough on consto and the ablative: http://dcc.dickinson.edu/grammar/latin/ablative-source-and-material
They're using nummus in a really unusual position here, where actual Roman currency like the sestertius (which everyone who's read Asterix knows) and the denarius (which everyone who knows Christian history knows) would fit better. The as is less known, of course. And we could learn about Juno, who rules the coins.
Iuno nummos regit.
Well, it makes more sense if you take into account the actual pronunciation rules. Apparently (take this with a grain of salt, because I'm still trying to research this), final m (like in crustulum or imperium) or nasal consonants followed by a fricative (so -nf or -ns) would nasalize and elongate the preceding vowels. So constat would be pronounced with the n "fusing" with the o, making it a longer vowel but with a nasal quality. Romance languages eventually dropped the nasalization altogether, which is why in Spanish, we have the word "costar".
Read up on William Sydney Allen's "Vox Latina" and look up "Classical Latin Vowel Nasalization" if you want to read more on it.