论文标题
从苍鹭三角形中建造一个无限的椭圆曲线家族2-Selmer等级1
Construction of an infinite family of elliptic curves of 2-selmer rank 1 from heron triangles
论文作者
论文摘要
鉴于任何积极的整数n，众所周知，始终存在具有理性侧a，b和c的三角形，使三角形的面积为n。假设Shafarevich-Tate群体有限，我们首先从某种类型的Heron Triangles中构建了一个无限的恒星椭圆曲线的家族。我们还明确地生产了一个单独的无限许多Heronian椭圆形曲线的家庭，其中2固定的等级位于1到3之间。
Given any positive integer n, it is well known that there always exist triangles with rational sides a, b and c such that the area of the triangle is n. Assuming finiteness of the Shafarevich-Tate group, we first construct a family of infinitely many Heronian elliptic curves of rank exactly 1 from Heron triangles of a certain type. We also explicitly produce a separate family of infinitely many Heronian elliptic curves with 2-Selmer rank lying between 1 and 3.
