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Ray class fields generated by torsion points of certain elliptic curves

✍ Scribed by Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon

Book ID: 118809263
Publisher: Springer US
Year: 2012
Tongue: English
Weight: 718 KB
Volume: 28
Category: Article
ISSN: 1382-4090
DOI: 10.1007/s11139-012-9396-4

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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