Not quite. That was the California. The Carpathia was the ship that did pick up the distress calls and was the first ship to make it to the area. Unfortunately they were too far away to get there before the ship went down but they picked up all the survivors, and an awful lot of the bodies.
oops
If this is set in 2040 that's just terrible, the only way we'd have interstellar travel by then is if some kindly aliens came along and just gave it us!
Hey it's sci-fi. When was the last time you didn't put your credulity on hold?