Norm and Trace of thej-invariants of Drinfeld Modules Associated to Hyperelliptic Curves Original Research Article

Letk/imageq(x) be a quadratic extension that is ramified over the unique pole ofx, and letAbe the integral closure of imageq[x] ink. Thenkis the function field analogue of an imaginary quadratic number field. A rank-one DrinfeldA-moduleφof generic characteristic is the analogue of an elliptic curve with complex multiplications by the full ring of integers of an imaginary quadratic number field. In this paper, we compute the degrees of the trace and norm down to imageq[x] ofj(φ), thej-invariant ofφ. Our results generalize previous ones wherekwas assumed to have genusg=1.