cURL for Windows can't make a secure connection to the Stack API

Question

I am using cURL for Windows.

I'm following separate advice and have just about no idea what I'm doing, but I know what I've done:

C:\...> curl http://api.stackexchange.com/2.1/sites
<garbage, probably encrypted>

C:\...> curl https://api.stackexchange.com/2.1/sites
curl: (60) SSL certificate problem: unable to get local issuer certificate
More details here: http://curl.haxx.se/docs/sslcerts.html

curl performs SSL certificate verification by default, using a "bundle"
 of Certificate Authority (CA) public keys (CA certs). If the default
 bundle file isn't adequate, you can specify an alternate file
 using the --cacert option.
If this HTTPS server uses a certificate signed by a CA represented in
 the bundle, the certificate verification probably failed due to a
 problem with the certificate (it might be expired, or the name might
 not match the domain name in the URL).
If you'd like to turn off curl's verification of the certificate, use
 the -k (or --insecure) option.

I haven't added any frills, but I do not have what you'd call a 'normal' installation; I've temporarily added the unzipped folder to my PATH, but it's on my desktop. I don't think this makes a difference but, again, I have no idea what I'm doing.

(If you're interested, I'm working on a Stack Exchange mode for Emacs.)

Answer 1

As you can see it is gzip

$ curl -I api.stackexchange.com/2.1/sites
HTTP/1.1 400 Bad Request
Cache-Control: private
Content-Length: 95
Content-Type: application/json; charset=utf-8
Content-Encoding: gzip

So

$ curl -s --compressed api.stackexchange.com/2.1/sites
{"items":[{"site_type":"main_site","name":"Stack Overflow","logo_url":"http://cd
n.sstatic.net/stackoverflow/img/logo.png","api_site_parameter":"stackoverflow","
site_url":"http://stackoverflow.com","audience":"professional and enthusiast pro
[...]

Tricky Tricky