On the class number divisibility of pairs of quadratic fields obtained from points on elliptic curves

Yoshichika Iizuka; Yutaka Konomi; Shin Nakano

doi:10.2969/jmsj/06820899

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

On the class number divisibility of pairs of quadratic fields obtained from points on elliptic curves

Yoshichika Iizuka, Yutaka Konomi, Shin Nakano

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Keywords: class number, quadratic field, elliptic curve

JOURNAL FREE ACCESS

2016 Volume 68 Issue 2 Pages 899-915

DOI https://doi.org/10.2969/jmsj/06820899

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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 ℚ(√D) and ℚ(√(mD)) with both class numbers divisible by l. Such quadratic fields are parametrized by rational points on a specified elliptic curve.

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