✦ LIBER ✦

Homomorphisms From the Group of Rational Points On Elliptic Curves to Class Groups of Quadratic Number Fields

✍ Scribed by R. Soleng

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 586 KB
Volume: 46
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1994.1013

No coin nor oath required. For personal study only.

✦ Synopsis

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. First we prove a conjecture concerning the order of ideals coming from rational points of infinite order on the curve. Then we describe how to construct families of quadratic number fields containing a subgroup of the ideal class group isomorphic to the torsion group of the curve. 1994 Academic Press, Inc.

📜 SIMILAR VOLUMES

On the Cyclicity of the Group of Fp-Rati

On the Cyclicity of the Group of Fp-Rational Points of Non-CM Elliptic Curves

✍ Alina Carmen Cojocaru 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 143 KB

Let E be an elliptic curve defined over Q and without complex multiplication. For a prime p of good reduction, let % E E be the reduction of E modulo p: Assuming that certain Dedekind zeta functions have no zeros in ReðsÞ > 3=4; we determine how often % E EðF p Þ is a cyclic group. This result was p

On the Number of Homomorphisms from a Fi

On the Number of Homomorphisms from a Finite Group to a General Linear Group

✍ Naoki Chigira; Yugen Takegahara; Tomoyuki Yoshida 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 144 KB

We study the number of homomorphisms from a finite group to a general linear group over a finite field. In particular, we give a generating function of such numbers. Then the Rogers-Ramanujan identities are applicable.

Refined Lower Bounds on the 2-Class Numb

Refined Lower Bounds on the 2-Class Number of the Hilbert 2-Class Field of Imaginary Quadratic Number Fields with Elementary 2-Class Group of Rank 3

✍ Elliot Benjamin; Charles J. Parry 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 125 KB

Let k be an imaginary quadratic number field with C k, 2 , the 2-Sylow subgroup of its ideal class group, isomorphic to ZÂ2Z\_ZÂ2Z\_ZÂ2Z. By the use of various versions of the Kuroda class number formula, we improve significantly upon our previous lower bound for |C k 1 , 2 | , the 2-class number of