Why is the class number of ℚ ( 11 3 ) even?

F. Lemmermeyer

Mathematica Bohemica (2013)

  • Volume: 138, Issue: 2, page 149-163
  • ISSN: 0862-7959

Abstract

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In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.

How to cite

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Lemmermeyer, F.. "Why is the class number of $\mathbb {Q}(\@root 3 \of {11})$ even?." Mathematica Bohemica 138.2 (2013): 149-163. <http://eudml.org/doc/252462>.

@article{Lemmermeyer2013,
abstract = {In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.},
author = {Lemmermeyer, F.},
journal = {Mathematica Bohemica},
keywords = {class number; pure cubic field; elliptic curve; class number; pure cubic field; elliptic curve},
language = {eng},
number = {2},
pages = {149-163},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Why is the class number of $\mathbb \{Q\}(\@root 3 \of \{11\})$ even?},
url = {http://eudml.org/doc/252462},
volume = {138},
year = {2013},
}

TY - JOUR
AU - Lemmermeyer, F.
TI - Why is the class number of $\mathbb {Q}(\@root 3 \of {11})$ even?
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 2
SP - 149
EP - 163
AB - In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.
LA - eng
KW - class number; pure cubic field; elliptic curve; class number; pure cubic field; elliptic curve
UR - http://eudml.org/doc/252462
ER -

References

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