论文标题
椭圆形曲线的同基因在功能场上
Isogenies of elliptic curves over function fields
论文作者
论文摘要
我们证明了两个有关椭圆曲线的椭圆形曲线的定理。第一个描述了$ j $ invariant在同一类中的高度的变化。第二个是“同一估计值”，它在两个同基因椭圆曲线之间的最小同等基因的程度上提供了明确的结合。我们还给出了这两个结果的几个推论。
We prove two theorems concerning isogenies of elliptic curves over function fields. The first one describes the variation of the height of the $j$-invariant in an isogeny class. The second one is an "isogeny estimate", providing an explicit bound on the degree of a minimal isogeny between two isogenous elliptic curves. We also give several corollaries of these two results.
