What form of ECC can we use to make sure our newly invented ECC based crypto-systems are quantum secure?
Traditional Elliptic Curve Cryptography (working in the group of points on an elliptic curve over a finite field) is vulnerable to an attack by a quantum computer running Shor's algorithm and is thus not considered a Quantum-Safe.

However there is a true Post Quantum Key Exchange algorithm which uses the mathematics of elliptic curves and is considered secure by experts who have studied it so far. This key exchange is known as Supersingular isogeny key exchange.