Hi HomerJ,
Officially there is no version that currently supports Java 11. With ALM 12.60 release and no java package being included within the installer, rumor is that this will allow the client to install and maintain versions of Java not officially supported in future patch releases (as they have done with other environmental specifics such as Linux and Citrix that as long as they meet the minimum requirements they will be allowed). As it is currently they do not support Java 11 in any version.
There is a case opened for this and tracking under QCCR1J101452. IF you have the capability to access their knowledge base, you can follow the progression here: https://softwaresupport.softwaregrp.com/doc/KM03333003
and sign up to have notifications sent to you when the issue is updated so you . will know as soon as it is resolved officially. Many are hoping for a quick resolution and have tried to install with Java 11 but the system will not allow the installation to complete as it reports an error of ''not finding a java installation'' even when it is directly pointed to in the installation setup. As of now it is not supported, and older versions wont support it either until they remove the java package from the installer as they have in 12.60.
Hope this helps,
Dan