Infinite rank of elliptic curves over $ℚ^{ab}$

• Autorzy: Bo-Hae Im , Michael Larsen
• Języki publikacji: EN

Abstrakty

EN

If E is an elliptic curve defined over a quadratic field K, and the j-invariant of E is not 0 or 1728, then $E(ℚ^{ab})$ has infinite rank. If E is an elliptic curve in Legendre form, y² = x(x-1)(x-λ), where ℚ(λ) is a cubic field, then $E(K ℚ^{ab})$ has infinite rank. If λ ∈ K has a minimal polynomial P(x) of degree 4 and v² = P(u) is an elliptic curve of positive rank over ℚ, we prove that y² = x(x-1)(x-λ) has infinite rank over $Kℚ^{ab}$.

Kategorie tematyczne

• 11G05: Elliptic curves over global fields
• 14H52: Elliptic curves

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 158
• Numer: 1
• Strony: 49-59

Daty

wydano

2013

Twórcy

autor

Bo-Hae Im

• Department of Mathematics, Chung-Ang University, 221 Heukseok-dong, Dongjak-gu, Seoul, 156-756, South Korea

autor

Michael Larsen

• Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.

Identyfikatory

DOI

10.4064/aa158-1-3