Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 45, Number 2 (2008), 375-390.
On the class numbers of certain number fields obtained from points on elliptic curves II
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.
Osaka J. Math., Volume 45, Number 2 (2008), 375-390.
First available in Project Euclid: 15 July 2008
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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