I answered a similar question herehere
You can download and clip a portion of the SRTM 30m DEM with one command with the elevation Python command line tool.
Install it and perform the self check with:
$ pip install elevation
Check if you have all the dependencies installed (mainly GDAL tools):
$ eio selfcheck
Download and clip a portion of the SRTM 30m DEM giving bounding box as WGS84 coordinates:
$ eio clip -o Rome-DEM.tif --bounds 12.35 41.8 12.65 42