Traffic Lights, Signs and Controls: First Red-Light-Camera Ticket. Fight or Pay

My question involves a traffic ticket from the state of: California

I have clean DMV (as in no points) and the priority is keeping it that way. Believe I'm eligible for traffic school.

Most Important Question
Am I remembering correctly that, if I choose to fight the ticket and I lose, my traffic school option is forfeit? Is that presently true?

DETAILS ON MY NOTICE

• Location of violation: Cedar Blvd. & Mowry Ave. NB, Newark, CA::Alameda County
• Date & time on my notice: 4/23/2017 at 3:18 AM
• non-commercial vehicle (correct)
• non-hazmat vehicle (correct)
• code & section 21453a
• Issuance & cert. of mailing dated 5/26/17
• 1st of 4 pictures: far shot of car in far right lane, wheels not in crosswalk, no other cars or people in sight...caption says speed is 21 mph
• 2nd of 4 pictures: far shot of car proceeding on right turn through crosswalk, no other cars/people in sight...caption says same speed less than 1 second later
• 3rd of 4 pictures: windshield shot shows Chevrolet logo and driver but front plate is not in frame, little blurry but a rational person would agree it's me
• 4th of 4 pictures: rear shot shows logo and "Cruze," too blurry to read reg. sticker but my plate # is clearly visible

ADDITIONAL DETAILS IN CASE THEY'RE RELEVANT

• It was a rental car with no other authorized drivers
• Don't remember if there was a No Right Turn sign posted and can't tell from photos....If relevant, I can try to find out using Google StreetView
• I've viewed the video online and cannot fault it except perhaps that, by itself, no identifying details of car or driver are discernible

Traffic Lights, Signs and Controls: First Red-Light-Camera Ticket. Fight or Pay