A Modular Curve of Level 9 and the Class Number One Problem

Details A Modular Curve of Level 9 and the Class Number One Problem A Modular Curve of Level 9 and the Class Number One Problem

2008-01-30

arxiv.org/abs/0801.4693v2

Mathematics

Number Theory

18 pages

Scientific paper

10.1016/j.jnt.2008.09.013

In this note we give an explicit parametrization of the modular curve
associated to the normalizer of a non-split Cartan subgroup of level 9. We
determine all integral points of this modular curve. As an application, we give
an alternative solution to the class number one problem.

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