Multi-modulus elliptic curve constructions provide only modest constant-factor security improvements, not exponential gains. Through formal analysis, we prove that distinct coprime moduli yield larger cyclic subgroups than single-modulus constructions, while identical moduli offer no asymptotic security improvement whatsoever. We examine the discrete logarithm problem in product groups and clarify common misconceptions about multi-modulus cryptographic designs. Our results show that while distinct moduli provide a structural advantage via increased subgroup order, the actual security gain is limited to a small constant-factor increase in attack complexity. This work provides rigorous bounds on the security properties of elliptic curve systems built over product rings and informs realistic expectations for cryptographic system design.