Determining the age of a supermassive black hole (SMBH) at the center of an elliptical galaxy is a challenging task, and there isn't a straightforward method to directly measure the age of a black hole itself. Black holes do not have a lifespan in the same way that stars do, as they are not fueled by nuclear fusion.
However, astronomers can estimate the age of the elliptical galaxy that hosts the SMBH using various techniques, such as studying the stellar populations within the galaxy, their chemical composition, and the overall structure. These methods provide insights into the formation and evolution of the galaxy, which can indirectly give us an idea of the age of the supermassive black hole.
Elliptical galaxies are generally considered to be older than spiral galaxies, and they are thought to have formed earlier in the universe's history. The age of an elliptical galaxy hosting a supermassive black hole can be estimated based on the ages of the stars within it. By studying the distribution of different stellar populations, astronomers can make inferences about the galaxy's formation history and estimate its age.
However, it's important to note that these age estimates come with uncertainties and assumptions. The formation and growth of supermassive black holes are complex processes that are still being studied, and our understanding of them is evolving. Therefore, the age of a supermassive black hole at the center of an elliptical galaxy is often inferred indirectly through the age estimation of the host galaxy itself, rather than being directly measured.