Abstract
Let $l$ be the prime $3,5$ or $7$ and let $m$ be a nonzero integer. We give a method for constructing an infinite family of pairs of quadratic fields ${\mathbb Q} \bigl(\sqrt D \big)$ and ${\mathbb Q} \bigl(\sqrt{mD} \big)$ with both class numbers divisible by $l$. Such quadratic fields are parametrized by rational points on a specified elliptic curve.
Citation
Yoshichika IIZUKA. Yutaka KONOMI. Shin NAKANO. "On the class number divisibility of pairs of quadratic fields obtained from points on elliptic curves." J. Math. Soc. Japan 68 (2) 899 - 915, April, 2016. https://doi.org/10.2969/jmsj/06820899
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