Abstract: Based on the Monte Carlo (MC) method and the fast Fourier transform micromagnetics (FFTM) method, the magnetization dynamics properties of Co nanorings with different parameter s of hyperelliptical curves were simulated. It is found that the hysteresis loops for hyperelliptic curved Co nanorings of different parameters s all exhibit "bistable" characteristics and have abundant transitional states. However, the hysteresis loops and spin configurations of the nanorings are influenced by the shape and sharpness of the inner edge of the system. Meanwhile, by simulating the spin configuration of the hyperelliptic curved Co nanorings, a reasonable explanation was made for the phenomena produced by different inner diameter edge shapes with different s. Further research shows that the parameter s of hyperelliptic curved Co nanorings is closely related to the external magnetic field required for the system to reach the saturated state. The step width of the hysteresis loop of the hyperelliptic curve also changes with parameter s, indicating that s has a significant impact on the stability of the “vortex state” in the hyperelliptic curve.