Files modified in last 30 min

I am using the below command to list the files with name core which are created in last 30min,

ls -ltr `find . -name "core*" -mmin -30`

I am getting the proper result when there is a file with name core,core1 but the issue coming when there is no core file as its listing other files,

ls -ltr `find . -name "core*" -mmin -30`
total 4
-rw-r--r-- 1 root msste 6 Nov  8 01:15 test.txt

Please let me know how to fix this.

Thanks in advance.