CDM and SIDM Interpretations of the Strong Gravitational Lensing Object JWST-ER1

van Dokkum et al. (arXiv: 2309. 07969) reported the discovery of JWST-ER1, a strong lensing object at redshift z2, using data from the James Webb Space Telescope. The lens mass within the Einstein ring is 5. 9 times higher than the expected stellar mass from a Chabrier initial mass function, indicating a high dark matter density. In this work, we show that a cold dark matter halo, influenced by gas-driven adiabatic contraction, can account for the observed lens mass. We also derive constraints on dark matter self-interacting cross section per particle mass /m. For /m0. 3~ cm²/g within a 10^13~M_ halo, the density profile is too shallow to be consistent with the measured lens mass of JWST-ER1, while /m0. 1~ cm²/g is well allowed. Intriguingly, self-interacting dark matter with /m0. 1~ cm²/g can simultaneously explain the dark matter density profile of early-type galaxies at redshift z0. 2, where adiabatic contraction is not observed overall.