How do you NOT check for primality when it is a necessary condition for the math to work?

[Layman806]

PyECC/ecc/elliptic.py

Line 96 in 667c62f

# coprimality is not checked here in favour of performance

I tried implementing the NIST proposed ECC curves, and using it, I found out that checking for coprimality leads to some inverses not existing due to gcd != 1. What do I do now? And how is this resolved in other applications implementating ECC.