HTTPS is used for secure communication over a computer network, and is widely used on the Internet. In HTTPS, the communication protocol is encrypted using Transport Layer Security (TLS) or, formerly, Secure Sockets Layer (SSL). The protocol is therefore also referred to as HTTP over TLS or HTTP over SSL.

For ELS61 series (PLS62-W, ELS61, ELS61-AUS, E, E2, ER2, US, USA): HTTP / SecureConnection over SSL version 3.0 and TLS versions 1.0, 1.1 and 1.2.

We support both only server verified and Mutual Authentication method on the module. 

Here is the document to tell you how to do HTTPS connection via module (using TCP/IP stack inside module)