我以Styx的名义起誓，即希腊神话中常出现的以冥河的名义起誓，的英文怎么说。

I swear by the name of Styx, namely the Greek mythology often appears in the name of the river to hades

I swear in the name of Styx........

but I think the name of the river is Acheron!

but I'm wrong
River Styx was a river which formed the boundary between Earth and the Underworld
Acheron was known as the river of pain, and was one of the five rivers of the Greek underworld