Elliptic Curves and Class Groups of Quadratic Fields
β Scribed by Buell, D. A.
- Book ID
- 120096396
- Publisher
- Oxford University Press
- Year
- 1977
- Tongue
- English
- Weight
- 172 KB
- Volume
- s2-15
- Category
- Article
- ISSN
- 0024-6107
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π SIMILAR VOLUMES
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
We show that the number of elliptic curves over Q with conductor N is < < = N 1Γ4+= , and for almost all positive integers N, this can be improved to < < = N = . The second estimate follows from a theorem of Davenpart and Heilbronn on the average size of the 3-class groups of quadratic fields. The f
Using the theory of elliptic curves, we show that the class number hΓ°ΓpΓ of the field QΓ° ffiffiffiffiffiffi ffi Γp p Γ appears in the count of certain factors of the Legendre polynomials P m Γ°xΓ Γ°mod pΓ; where p is a prime 43 and m has the form Γ°p Γ eΓ=k; with k ΒΌ 2; 3 or 4 and p e Γ°mod kΓ: As part