I came across this answer now (2014) and some links are out of date.
For all the general information (all platforms) you can start reading http://curl.haxx.se
There is a download wizard to help you choose the most current and appropriate file or binary file at the moment http://curl.haxx.se/dlwiz/ . To answer this question, "libcurl" must be selected in the wizard. At the moment, win64 only seems to be available in the cygwin version, so go to win32 until this changes.
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