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

100%

Im B.-H., Larsen M.

Acta Arithmetica

2013

tom 158

nr 1

49-59

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 $Kℚ^{ab}$.

Normalizers of intermediate congruence subgroups of the Hecke subgroups

81%

Im B.-H., Jeon D., Kim C. H.

Open Mathematics

2017

tom 15

nr 1

787-799

For a square-free positive integer N, we study the normalizer of ΓΔ(N) in PSL2(ℝ) and investigate the group structure of its quotient by ΓΔ(N) under certain conditions.

Ograniczanie wyników

1 Acta Arithmetica

1 Open Mathematics

2 Im B.-H.

1 Jeon D.

1 Kim C. H.

1 Larsen M.

1 2017

1 2013

Wyniki wyszukiwania

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

Normalizers of intermediate congruence subgroups of the Hecke subgroups