论文标题
椭圆曲线的发电机$ e _ {（p，q）}：y^2 = x^3 -p^2x + q^2 $
Generators for the elliptic curve $E_{(p,q)} : y^2 = x^3 - p^2x + q^2$
论文作者
论文摘要
令$ \ {较早的工作表明，椭圆曲线$ e _ {（p，q）} $在所有$ p，q> 5 $和两个独立点上至少排名两个。本文表明，在条件下，可以将两点扩展到$ e _ {（p，q）} $的基础上，这有信心我们将完全恢复。
Let $\{E_{(p,q)}\}$ be a family of elliptic curves over a rational field such that we have $E_{(p,q)} : y^2 = x^3 - p^2x + q^2$, where $p$ and $q$ are prime numbers greater than five. Earlier work showed that the elliptic curve $E_{(p,q)}$ had ranked at least two for all $p, q > 5$ and two independent points. This paper shows that two points that can be extended to a basis for $E_{(p,q)}$ under conditions are confident that we will fully recover.
