Osaka Journal of Mathematics

On the class numbers of certain number fields obtained from points on elliptic curves II

Atsushi Sato

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Abstract

We construct a family of cyclic extensions of number fields, in which every finite place is unramified, from an elliptic curve with a rational torsion point. As an application, we obtain such polynomials $F(X)$ of rational coefficients that have the following property: For a rational number $\xi$ chosen at random, the class number of the field generated by the square root of $F(\xi)$ is ``often'' divisible by 3, 5 or by 7.

Article information

Source
Osaka J. Math., Volume 45, Number 2 (2008), 375-390.

Dates
First available in Project Euclid: 15 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1216151104

Mathematical Reviews number (MathSciNet)
MR1864464

Zentralblatt MATH identifier
1197.11148

Subjects
Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11G05: Elliptic curves over global fields [See also 14H52] 11G07: Elliptic curves over local fields [See also 14G20, 14H52]

Citation

Sato, Atsushi. On the class numbers of certain number fields obtained from points on elliptic curves II. Osaka J. Math. 45 (2008), no. 2, 375--390. https://projecteuclid.org/euclid.ojm/1216151104


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