NO, it is not finished.
The anime finished after the manga:
Anime finished: April 13, 2006
Manga finished: March 25, 2006
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Anime - Base
Release date: November 04, 2004
Anime - Sequel
Release date: January 22, 2006
Ginyuu Mokushiroku Meine Liebe follows five noble students – Orpherus, Eduard, Camus, Lui, and Naoji – at the elite Rozenstolz academy in the European kingdom of Kuchen.
These five are part of the prestigious Strahl class, training them for potential advisory roles to the king.
As they navigate their studies and personal lives, they become entangled in political intrigue and conspiracies within the kingdom.
They must confront corrupt officials, secret agents, and various threats from those who seek to destabilize Kuchen and harm the king, all while trying to uncover the truth and protect their country.
An English writer named Isaac also gets involved in the unfolding events.