In English there exists the proposition modulo (see also the Wiktionary entry) or modulo the fact. Any of these, however, are not proper from English, but have their origin in mathematics, presumably from the expression
p≡q mod n.
Parenthetically, the fact
6 ≡ 2 (mod 4)
is extended to more general (i.e. non-mathematical situations), where you can say:
All mammals, modulo the monotremes, give birth to live young. (Example taken from Wiktionary's link above).
Now to the actual question, which is constrained to math. In German one uses the same sign,
X/Y for X mod Y. While usual expressions involve only mathematical objects, one usually needs to write them down with words (here is where the question might be valid here). That is, it turns out that in concrete cases, when the involved expressions have a proper name, it doesn't sound too educated if one mentions the letters. Let me bore you with a last line specifying that:
Consider F/Σn where Σn has a proper name, die symmetrische Gruppe. If you want to read out or write down that in German, then modulo should be a preposition. I'd read it as:
"ef modulo der symmetrischen Gruppe"
Consider a≡b mod n, where a,b,n are just numbers. Then after some lines it's valid to state that as: "[hier erwähnt man n]...und modulo diese(r) Zahl, ist a gleich b"
Which case should I use for modulo? (I'm going with genitive because of the answer given here, but I'd need help from an expert.)