The California Vehicle Code (CVC) provides that if you have attended an 8 hour class in the past 12 months (from your violation date), you CAN go back to traffic school for 12 HOURS, at the discretion of a judge (not to be confused with the automatic 18 months non eligibility the court of your last traffic school says it allows).
41501. The court may order a continuance of a proceeding against a person, who receives a notice to appear in court for a violation of any statute relating to the safe operation of a vehicle, in consideration for attendance at a licensed school for traffic violators, a licensed driving school, or any other court-approved program of driving instruction, and, after that attendance, the court may dismiss the complaint under the following conditions:
(a) If the offense is alleged to have been committed within 12 months of another offense which was dismissed under this section, the court may order the continuance and, after the attendance, dismiss the complaint. The court may order attendance at a licensed school for traffic violators which offers a program of at least 12 hours of instruction.
(b) If the offense is not alleged to have occurred within 12 months of another offense which was dismissed under this section, the court may order the continuance and, after the attendance, dismiss the complaint if the attendance is at any of the types of schools or programs that the court directed pursuant to Section 42005 at the time of ordering the continuance. This course will cost more money than the 8 hour class (usually $10 more), and will NOT be MASKED from the insurance company that you attended.
What will appear on your DMV record is, "T/S violation Date"... which means your case was dismissed by traffic school. Can an insurance company raise you because they know you went to traffic school? NOPE. Can a FUTURE insurance company penalize you for knowing this? YEP. But it's still a good idea to go and keep the points off your record towards losing your license.