Oracle EBS 12.1.3 is certified with Oracle JDK 1.7.0_25 (64-Bit) on Linux x86-64 Red Hat Enterprise
From looking at the Certification Matrix in MOS: I see that JDK 1.7.0_25b 15 (64bit) is ceritified to run on Oracle E-Business Suite release 12.1.3 on a Linux x86-64 Bit Platform.
But looking at the following 2 Documents I see that forms and reports are not Supported on 64 Bit.
Note:1467892.1 JDK 7.0 Latest Update with Oracle E-Business Suite Release 12.0 and 12.1
ie:
Step 3.3: Download Latest JDK 7.0 Update
Click on the appropriate link below to download the JDK from the site that corresponds to the operating system being used on the application tier node. Download the 32-bit JDK, not the Java Runtime Environment (JRE). Do not choose the 64-bit version, which is not supported.