A CERTAIN FAMILY OF SUPERELLIPTIC CURVES ASSOCIATED WITH -EXTENSION
Let p be a prime and k be a field containing a primitive pth root of unity. We give a general way of construction of cubic polynomials with coefficients in k such that all of the ranks of Jacobian variety of the curves over are Moreover for by specializing t, we obtain elliptic curves such that are rational numbers, their ranks are at least one over Q, and each two are not isomorphic over Q.
superelliptic curve, Jacobian variety, twist theory.