I know it's been a long time since you wrote this but I live in Rio Rancho NM and I just saw what you're describing. It was a red light, no flashing lights whatsoever, that rose up from the distance near the horizon and curved to the right. It then continued up, almost straight up. After that it seemed to be travelling away from me and disappeared. The whole thing from start to finish was about 5 mins or so, which was a bit fast to be a commercial airliner. I know that there are Military Bases here so I guess that's one explanation but I'm not too sure that's what it was.