  The development of secure cryptographic protocols and the subsequent attack
mechanisms have been placed in the literature with the utmost curiosity.
  While sophisticated quantum attacks bring a concern to the classical
cryptographic protocols present in the applications used in everyday life, the
necessity of developing post-quantum protocols is felt primarily.
  In post-quantum cryptography, elliptic curve-base protocols are exciting to
the researchers.
  While the comprehensive study of elliptic curves over finite fields is well
known, the extended study over finite rings is still missing.
  In this work, we generalize the study of Weierstrass elliptic curves over
finite ring $\mathbb{Z}_n$ through classification.
  Several expressions to compute critical factors in studying elliptic curves
are conferred.
  An all-around computational classification on the Weierstrass elliptic curves
over $\mathbb{Z}_n$ for rigorous understanding is also attached to this work.
