how do i find my serial number?

From the Related Article above.

If you don't have your device

There are several places to check that might show the serial or IMEI/MEID number.

1. Go to appleid.apple.com in a web browser.
2. Sign in with the Apple ID that you use on your device. 
3. Choose the Devices section. To see the serial and IMEI/MEID number, select the device.

If you still need help, here's what to try next:

• 
  
• Do you have a different device with iOS 10.3 or later that's signed in to your Apple ID? On that device, go to Settings > [Your name]. Scroll down to see any devices signed in with your Apple ID. To view the serial and IMEI/MEID number, tap the device name.
• Do you still have your device's original package? Find the serial number and IMEI/MEID on the barcode:
• 

Eric Root, above, said it better than what I had so mine is deleted.