Class numbers of quadratic fields and Shimura's correspondence (Q1124632)
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scientific article; zbMATH DE number 4112723
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Class numbers of quadratic fields and Shimura's correspondence |
scientific article; zbMATH DE number 4112723 |
Statements
Class numbers of quadratic fields and Shimura's correspondence (English)
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1990
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A formula for the 3-rank of the class group of an imaginary quadratic field \({\mathbb{Q}}(\sqrt{D})\) in terms of \(\sqrt{-3}\)-descent on the elliptic curve \(DY^ 2=4X^ 3-27\) is established. Explicit calculation of Shimura's correspondence proves consistence of this result with the Birch and Swinnerton-Dyer conjecture.
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3-rank of the class group of an imaginary quadratic field
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descent elliptic curve
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Shimura's correspondence
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Birch and Swinnerton-Dyer conjecture
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0.94559705
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0.94187444
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0.9391338
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0.93834597
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0.93796146
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0.93238986
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0.93157923
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