Judging from your location of NYC, there is no plea bargaining. The only way to avoid the points is to be found not guilty. If you received it anywhere other than the 5 boros, you may be able to plea bargain.
There is no plea bargaining in NYC Traffic Court so your options are to plead guilty or go to trial. If you want to go to trial I suggest you hire a local Traffic Court lawyer who regularly appears there.
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I agree with the above answers. If you were not in one of the boroughs you can take a plea. Otherwise, to avoid these points, you're going to go to trial.
If you think $230 is expensive a lawyer is even more. We cannot give you a legal treatise here online as to how to defend your ticket. Best of luck!