<p>In recent years, cryptographic research has seen a surge of interest in post-quantum cryptography driven by the potential threat that quantum computers pose to traditional public-key cryptosystems. Isogeny-based cryptography is a promising method in post-quantum cryptography, relying on the computational challenge of calculating isogenies, which are specific mappings between elliptic curves. The efficiency of isogeny computations is vital for real-world cryptographic applications. However, computing isogenies, especially with large parameters, can be very resource intensive. To overcome this challenge, we purpose an efficient method for computing odd-degree isogenies on certain form of an elliptic curves by employing an auxiliary coordinate. Our work appears to bridge the gap in computational efficiency for odd-degree isogenies, especially in terms of reducing the complexity of the isogeny computations when compared to traditional affine and projective methods. The derived formula is more efficient than affine and projective cases. We also analyse the algebraic complexity of these calculations and compare them to alternative formulae. Additionally, we evaluate the runtimes for isogeny computation across different prime numbers and compare them with other elliptic curve model to check the performance. At last, we suggest potential avenues for future work.</p>