The Mordell-Weil group of certain abelian varieties defined over the rational function field
An explicit method of construction of a family of abelian varieties each member of which has a large Mordell-Weil rank is given. For example, the following result is obtained: The elliptic curve \(E_ t:(t^ 6+2t^ 4+2t^ 2+1)y^ 2=x^ 3+2x^ 2+2x+1\) has Mordell-Weil rank \(\geq 2\) for every \(t\in\mathbb{Q}-\{0,\pm 1\}\). Further, an example of an elliptic curve defined over a function field of one variable is constructed such that its Mordell-Weil group is of arbitrarily high rank.
scientific article; zbMATH DE number 146176