In this paper, we introduce the notion of the simplest cubic fields, and the associated elliptic curves, hyperelliptic curves. Next, we compute ranks of the elliptic curves by using hyperelliptic curves.
Jung Soo Kim. "Efficient computation of rank of elliptic curves using hyperelliptic curves associated with the simplest cubic fields." Proc. Japan Acad. Ser. A Math. Sci. 76 (9) 129 - 131, Nov. 2000. https://doi.org/10.3792/pjaa.76.129