论文标题
欧几里得的几何形状和椭圆形曲线
Euclidean Geometry and Elliptic Curves
论文作者
论文摘要
在本文中，我们证明了一些几何图形之间的亲密关系和具有正等级的椭圆曲线家族。这些几何图包括\ textIt {\ textbf {heron triangles}}，\ textit {\ textbf {brahmagupta quadrilitalals}}}和\ textit {\ textbf {bicentric Quadrilillilalals}}}。首先，我们研究了这些数字的重要特性，然后利用这些特性，我们表明了如何构建具有不同扭转亚组的不同正等级的各种椭圆曲线家族。
In this paper, we demonstrate the intimate relationships among some geometric figures and the families of elliptic curves with positive ranks. These geometric figures include \textit{\textbf{Heron triangles}}, \textit{\textbf{Brahmagupta quadrilaterals}} and \textit{\textbf{Bicentric quadrilaterals}}. Firstly, we investigate the important properties of these figures and then utilizing these properties, we show that how to construct various families of elliptic curves with different positive ranks having different torsion subgroups.
