On the class numbers of certain number fields obtained from points on elliptic curves II
Sato, Atsushi
Osaka J. Math., Tome 45 (2008) no. 1, p. 375-390 / Harvested from Project Euclid
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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.
Publié le : 2008-06-15
Classification:  11R29,  11G05,  11G07 
@article{1216151104,
     author = {Sato, Atsushi},
     title = {On the class numbers of certain number fields obtained from points on elliptic curves II},
     journal = {Osaka J. Math.},
     volume = {45},
     number = {1},
     year = {2008},
     pages = { 375-390},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1216151104}
}

Sato, Atsushi. On the class numbers of certain number fields obtained from points on elliptic curves II. Osaka J. Math., Tome 45 (2008) no. 1, pp.  375-390. http://gdmltest.u-ga.fr/item/1216151104/