Construction of Number Fields of Odd Degree with Class Numbers Divisible by Three, Five or by Seven
Open Access
- 1 January 2010
- journal article
- Published by Graduate School of Information Sciences, Tohoku University in Interdisciplinary Information Sciences
- Vol. 16 (1) , 39-43
- https://doi.org/10.4036/iis.2010.39
Abstract
We introduce a simple way to construct a family of number fields of given degree with class numbers divisible by a given integer, by using the arithmetic theory of elliptic curves. In particular, we start with an elliptic curve defined over the rational number field with a rational torsion point of order l ∈ {3,5,7}, and show a way to construct infinitely many number fields of given odd degree d ≥ 3 with class numbers divisible by l.Keywords
This publication has 2 references indexed in Scilit:
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- Fundamentals of Diophantine GeometryPublished by Springer Nature ,1983