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Hyperelliptic curves and homomorphisms to ideal class groups of quadratic number fields

✍ Scribed by Tormod Kalberg Sivertsen; Ragnar Soleng

Book ID: 113731036
Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 147 KB
Volume: 131
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2011.05.002

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The main purpose of this paper is to prove that there is a homomorphism from the group of primitive points on an elliptic curve given by an equation \(Y^{2}=X^{3}+a_{2} X^{2}+a_{4} X+a_{6}\) to the ideal class group of the order \(\mathbb{Z}+\mathbb{Z} \sqrt{a_{6}}\). Two applications are given. Fir

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