How to cite "Crelle's Journal"

I usually see "J. Reine Angew. Math." without "Crelle".

MathSciNet has citation information in the form of BibTeX entries; for references indexed there, I recommend going with that. (Indeed if you use BibTeX you can just download the bibliographic information without writing it out again.)

I agree with Anonymous. I think you are misreading the website. They are not telling you say "Crelle's journal" when you cite. If you click the cite link on the journal homepage, they give you something like this (for APA format):

Journal für die reine und angewandte Mathematik. Berlin, Boston: De Gruyter. Retrieved 26 Sep. 2016, from http://www.degruyter.com/view/j/crll

without the nickname.

That said, it's pretty weird that the cite options you get are APA, MLA and Chicago as none of them are ever used in math. It's already pretty weird to use the full journal name, rather than the standard abbreviation. I usually use MathSciNet to make my bibliographies, as Anonymous recommends.

Note: I have seen people include (Crelle's Journal) in citations on their CV or website, which is okay though perhaps not common, but I wouldn't do it for a bibliography (edit: not to say it doesn't happen, as other answers point out).

For citing most any mathematics journal there is an easy way to get what the common way to cite it is: look up the (short) title in MathSciNet or zbMATH, the latter allows limited access without subscription (almost always they use the same).

If you want to be on the safe side use whatever is given there as (short) title. For the current case this is "J. Reine Angew. Math."

It is true that for this journal specifically mention of its founder's name Crelle is somewhat common, so if you want to you might include it. It is sufficiently official as for zbMATH mentioning "Crelle's Journal" as parallel title.

A reason for doing this could be that some might recognize it more directly than under its real name, but this is (if at all) relevant for a CV more than for a bibliography.

I'd say if you really want to you could use Crelle's Journal as the journal name. It might get changed in copy-editing though. But if you are not convinced it is a good idea just don't. No one should find it strange if you do not use it.

To get a feeling how common it is to use it nowadays one can search for example arXiv with fulltext search. One gets around 250 hits for Crelle. Mostly they mean the journal. A cursory look shows that:

• the format to include Crelle's journal or Crelle in parenthesis to complement J. Reine Angew. Math. or something similar is no uncommon (as mentioned by Andreas Blass).

• to use only Crelle's journal is rare but nevertheless is still done sometimes.

In this process I noted that the DOIs of the journal contain the string "crelle."