How can you change Custom URL Base using REST API?

For changing the Custom URL Base using the REST API, you may use following API (requires Artifactory 3.9.0 and above):

 ‘PUT at /api/system/configuration/baseUrl‘ 

e.g curl -X PUT http://host:port/artifactory/api/system/configuration/baseUrl -d ‘http [s] ://url’ -uuser:password -H “Content-type: text/plain” 

Furthermore, you may use General Configuration” API  to check the current configuration.