Amtrak owns most of the Northeast Corridor[0] - except the section from New Haven to New Rochelle, which is owned by the State of CT and Metro North. Incidentally, there are the sections where the Acela slows to a crawl. This is also the most viable corridor for Amtrak.

They also own sections of other lines - including the New Haven-Springfield line[1].

[0]: https://en.m.wikipedia.org/wiki/Northeast_Corridor

[1]: https://en.wikipedia.org/wiki/Hartford_Line