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

Bo-Hae Im, and Michael Larsen. "Infinite rank of elliptic curves over $ℚ^{ab}$." Acta Arithmetica 158.1 (2013): 49-59. <http://eudml.org/doc/279299>.

@article{Bo2013,
abstract = {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 $Kℚ^\{ab\}$.},
author = {Bo-Hae Im, Michael Larsen},
journal = {Acta Arithmetica},
keywords = {elliptic curves; Mordell-Weil group; Hilbert irreducibility},
language = {eng},
number = {1},
pages = {49-59},
title = {Infinite rank of elliptic curves over $ℚ^\{ab\}$},
url = {http://eudml.org/doc/279299},
volume = {158},
year = {2013},
}

TY - JOUR
AU - Bo-Hae Im
AU - Michael Larsen
TI - Infinite rank of elliptic curves over $ℚ^{ab}$
JO - Acta Arithmetica
PY - 2013
VL - 158
IS - 1
SP - 49
EP - 59
AB - 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 $Kℚ^{ab}$.
LA - eng
KW - elliptic curves; Mordell-Weil group; Hilbert irreducibility
UR - http://eudml.org/doc/279299
ER -