If you can sit for long periods, run & swim then I do not see how your 'slightly curved discs' will prevent you from the safe operation of an Aircraft.
You will have a general musculoskeletal assessment by the AME at the initial Class 1. I suggest that you fully disclose your history on the forms (facts and diagnosis by any clinicians only) and if you have a copy of the CT scan take it with you. The AME/CAA may request that you see a specialist just to confirm that your back is in good health or he may just conduct the standard musculoskeletal examination and if he is happy that will be it.
The guidance for what to expect for the musculoskeletal exam can be found here :
https://www.caa.co.uk/Aeromedical-Ex...e-material-GM/
I am not a medical professional and this is my laymans interpretations of the assessment criteria and your history. My feeling is that you will not be 'stumped' when applying based on you now being in good health but you may get a deferral which is not anything to worry about, more a compliance with regulatory requirements.
Good luck and let us know how you get on
