First Time Speeding Ticket NYC

Hi there, I was recently pulled over for the first time and given a speeding ticket for allegedly going 73 in a 50. I genuinely don’t think I was going 73. I have dashcam footage that shows I was going the flow of traffic. I was in the left lane and a white car was in front of me, he moved over to the middle lane and I didn’t pass him at all. About 5 seconds later I see a NY highway patrol car sitting on the side of the road, I obviously let off the gas and brake a little bit, but I it didn’t matter because he already started pulling out. I also have a radar detector (they are legal here in NY) which picks up all forms of singles including LiDAR, that didn’t go off at all. This equates to 6 points on my license and being a 20 year old male driver, insurance will likely go through the roof. I would like to fight this even to hopefully get the points reduced. Any thoughts on this?