It is The Dead Christ in the Tomb (1521-1522), by Hans Holbein the Younger, which Dostoevsky saw in the museum in Basel and which appears in The Idiot as a copy hanging on a door in Rogozhin's house: a Christ just taken down from the cross, with no promise of resurrection.
In Part Two, the prince sees the copy and says to Rogozhin: "Why, this painting could make someone lose his faith!" and Rogozhin answers: "And it does." Instead of arguing, the prince answers Rogozhin's question about God with a scene he once saw: the peasant woman who crosses herself because the baby smiled for the first time.
In Part Three, Hippolyte describes the same painting in his Explanation: "There is not a word of beauty in it; it is, entirely, the corpse of a man who endured endless torments." And he asks: "How could they believe, looking at a corpse like that, that this martyr would rise again?" For him, nature is a machine that grinds down even the best it has created.
The book does not refute the argument: Hippolyte's shot misfires for a technical reason, and the guests laugh. There are two readings: the painting is the novel's strongest attack on faith, or it is the point that forces faith to justify itself through life, and not through theory.