论文标题
$ \ mathbb {q}（\ sqrt {3p}，\ sqrt {m-21pn^{2}}）$的$ \ mathbb {q}的类别划分。
Class number divisibility of $\mathbb{Q}(\sqrt{3p}, \sqrt{m-21pn^{2}})$ constructed from elliptic curves of $2$-Selmer rank exactly $1$
论文作者
论文摘要
数字字段的班级数字划分问题是代数数理论中的经典问题之一，该问题源自高斯的班级猜想。椭圆曲线上的点之间的关系与数字字段的班级数字可划分之间的关系已经通过各种数学家的作品进行了探索。在这里，我们明确地构建了从某种类型的椭圆曲线点产生的双方域的未经隔离的Abelian扩展。此外，我们还以$ 1 $的价格显示了上述椭圆曲线的$ 2 $ - Selmer等级，我们还建立了一个无限的双季度领域，该领域均匀。
The class number divisibility problem for number fields is one of the classical problems in algebraic number theory, which originated from Gauss' class number conjectures. The relation between the points on an elliptic curve and class number divisibility of a number field has been explored through the works of various mathematicians. Here, we explicitly construct an unramified abelian extension of a bi-quadratic field generated from points of a certain type of elliptic curve. Moreover, showing the $2$-Selmer rank of the said elliptic curve as $1$, we also construct an infinite family of bi-quadratic fields of even class number.
