The fastest way to install any Elixir and OTP version on your system is to use the install scripts as explained in the documentation.

It is as easy as (on mac or linux):

$ curl -fsSO https://elixir-lang.org/install.sh
$ sh install.sh elixir@1.18.0 otp@27.1.2
$ installs_dir=$HOME/.elixir-install/installs
$ export PATH=$installs_dir/otp/27.1.2/bin:$PATH
$ export PATH=$installs_dir/elixir/1.18.0-otp-27/bin:$PATH
$ iex

On Windows, when you use PowerShell, you can do this:

curl.exe -fsSO https://elixir-lang.org/install.bat
.\install.bat elixir@1.18.0 otp@27.1.2
$installs_dir = "$env:USERPROFILE\.elixir-install\installs"
$env:PATH = "$installs_dir\otp\27.1.2\bin;$env:PATH"
$env:PATH = "$installs_dir\elixir\1.18.0-otp-27\bin;$env:PATH"
iex.bat

If you just want to install the latest version, you can do this:

$ curl -fsSO https://elixir-lang.org/install.sh
$ sh install.sh elixir@latest otp@latest