Thank you for your answer @adam !
Indeed, the site seems to be down : according to https://www.isitdownrightnow.com/srtm.csi.cgiar.org.html it’s been down since more than a week (I don’t know how this information is accurate through).
Since my main use is in mountains range, I think it’s best that I keep elevation data.
Using the “gmted” value did the trick!