在椭圆曲线的研究中,对于给定椭圆曲线,求它的秩是一个重要的课题.利用Shioda的方法证明了对于定义在函数域k(t)上的一类形如y2=z(x-atm)(z—btn)椭圆曲线的秩为0.
It is one of important subjects to compute the rank for a given elliptic curve in the study of ellip- tic curve. We prove that the rank of a class of the elliptic curve over function field k(t) of the form y2= x(x-atm) (x-btn) is zero by the method of shioda.