I am looking to test some properties of elliptic curves and I would like to have a variety of different families to test. I was wondering if there was, say, a catalogue of the different interesting families of elliptic curves that have been found.
Some types of families I am interested in would be: families of high rank, families of a given rank, one-parameter families, or families of even rank.
Thank you in advanced.
Without knowing exactly what properties you would like to test I hope the following will be of some help.
The best reference for families of high rank is the tables by Andrej Dujella. The tables are available from his web page here and are very much up-to-date as he is himself a researcher of the subject. If you dig into the very extensive bibliography there, you will find many families of different rank.
Also, John Cremona has tabulated all elliptic curves of conductor $< 350000$. See his web page here or lmfdb.org.