In the present study, the flow and acoustic characteristics of an aerospike nozzle supersonic jet at a Nozzle Pressure Ratio (NPR) = 3, three Temperature Ratios (TR) = 1, 3, 7 and two Swirl Numbers S = 0.10, 0.20 are presented. Implicit Large Eddy Simulations (ILES) are deployed to simulate the aerospike nozzle flow. The far-field aeroacoustic signature is computed based on the Ffowcs Williams-Hawkings (FWH) equation. In the vicinity of the aerospike bluff body, a shock-cell structure is formed for all the configurations. The shock strength and length as well as the pressure fluctuations are primarily affected by the TR in that jet region. The supersonic flow reattaches further downstream towards the aerospike bluff body as the TR increases at a fixed Swirl Number. This influences in particular the flapping motion of the annular shock-cell structure. The latter is characterized by power spectral density of the radial velocity at well-chosen monitoring points in that region. Subsequently, two-point cross-correlations in the annular jet shear layer are computed to detect azimuthal jet modes. The azimuthal jet excitation increases in amplitude with increasing Swirl Number S, leading to high Sound Pressure Levels at the Strouhal numbers observed. Downstream of the aerospike bluff body, a short circular shock-cell structure is observed at Swirl Number S = 0.10 for higher TR while the jet remains annular in the cold case. At S = 0.20, fewer shock cells are formed downstream of the aerospike bluff body. The shortening of the shock-cell structure leads to screech elimination at both Swirl Numbers. Further crosscorrelations for the axial velocity in the jet shear layers show supersonic convection velocities at Temperature Ratios (TR) = 3 and 7 for both Swirl Numbers which confirms the presence of Mach waves observed in the near-field snapshots. The Mach wave radiation features a slight helical propagation pattern in contrast with the baseline case without swirling motion. Furthermore, a skewness larger than 0.4 and a positive kurtosis of the pressure signals along the Mach wave radiation lines indicate crackle noise at TR7. The far-field spectra computed with the Ffowcs Williams-Hawkings equation display mixing noise only for S = 0.10. In the cold cases, high SPL are detected in agreement with the Broadband Shock-Associated Noise (BBSAN) central frequencies which were computed using the annular and circular shock-cell length. Additionally, high SPL are obtained due to Mach wave propagation, at the Strouhal numbers of the azimuthal modes and of radial motion of the annular shock-cell structure.