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 ξ chosen at random, the class number of the field generated by the square root of F(ξ) is "often" divisible by 3, 5 or by 7.
|Number of pages||16|
|Journal||Osaka Journal of Mathematics|
|Publication status||Published - 2008 Jun 1|
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