Abstract
Let $l$ be the prime $3$, $5$ or $7$, and let $m_{1}$,~$m_{2}$, $n_{1}$ and $n_{2}$ be non-zero rational numbers. We construct an infinite family of pairs of distinct quadratic fields $\mathbb{Q}(\sqrt{m_{1}D+n_{1}})$ and $\mathbb{Q}(\sqrt{m_{2}D+n_{2}})$ with $D\in\mathbb{Q}$ such that both class numbers are divisible by $l$, using rational points on an elliptic curve with positive Mordell-Weil rank to parametrize such quadratic fields.
Citation
Yoshichika IIZUKA. Yutaka KONOMI. Shin NAKANO. "An Application of the Arithmetic of Elliptic Curves to the Class Number Problem for Quadratic Fields." Tokyo J. Math. 44 (1) 33 - 47, June 2021. https://doi.org/10.3836/tjm/1502179314
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