This summer there are hourly trains during the morning going from Copenhagen to Hamburg (including a connecting Copenhagen-Padborg train to the ICE-T Frankfurt service) and during lunchtime going from Hamburg til Copenhagen.
From Copenhagen
5:22 (seasonal train)
6:22 (RJ to Prague)
7:22 (seasonal train)
8:22
9:22 (to Padborg, connecting to ICE 1187)
10:22 (RJ to Prague)
and then every two hours until 18:22 + 23:35 to Prague (seasonal)
From Hamburg Hbf
6:50
8:55
9:47 (ICE 1186 to Padborg, connecting train to Copenhagen)
10:53
11:52 (seasonal train)
12:28 (RJ from Prague, via Altona)
13:50 (seasonal train)
14:53
16:28 (RJ from Prague, via Altona)
18:50
22:28 (RJ from Prague, via Altona, seasonal).