Great question — answering as the UphillTech team:
I don't think there are any student-specific discounts, except that you can get the BahnCard about 1/3rd off. But as you say, the BahnCard is for people who travel frequently, not for single trips. Other ways to save money: Book your ticket as early as possible - there are limited quotas of cheaper tickets available if you do so. Use the Quer-Durchs-Land ticket , to travel as far as you can on a single day for 44 EUR - but you can only use local trains. Up to 4 people can accompany you for 6 EUR each. The Schönes-Wochenende-Ticket works the same, but only on weekends, and it's valid for up to 5 people and costs 42 EUR. The Länder-Tickets work the same but are restricted to a single state,...
Full answer by Michael Borgwardt: https://travel.stackexchange.com/a/22242 (CC BY-SA 3.0).
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