The Jenkins website shows for LTS versions:

• 1.596.2 (2015/03/23)
• 1.596.1 (2015/02/28)

Our installed Jenkins version is 1.580.3 (2015/01/27)
Thus, at "Manage Jenkins", a new version of Jenkins should be visible for download.
But there is nothing visible.

Plugin updates are shown regularly and an update of the plugins work without any problems.