I believe elliptic curves aren't broken by factoring. You might be confused with shor's algorithm. That is a quantum-algorithm that breaks both elliptic curves

I believe elliptic curves aren't broken by factoring. You might be confused with shor's algorithm. That is a quantum-algorithm that breaks both elliptic curves and RSA. It doesn't break elliptic curve crypto by factoring numbers. Instead, it breaks them by solving the discrete logarithm problem.