Positive rank quadratic twists of four elliptic curves

Cited 2 time in webofscience Cited 0 time in scopus
  • Hit : 360
  • Download : 0
Let K be a number field and E-i/K an elliptic curve defined over K for i = 1, 2, 3, 4. We prove that there exists a number field L containing K such that there are infinitely many d(k) is an element of L-x/(L-x)(2) such that E-i(dk)(L) has positive rank, equivalently all four elliptic curves E-i have growth of the rank over each of quadratic extensions L-k := L(root d(k)), more strongly, for any, i(1), i(2), ... , i(m). rank (E-i(l(i1) .. L-m)) > rank(E-i(L-i1 ... Lim-1)) > ... >rank(E-i(L-i1)) > rank(E-i(L)). We also prove that if each elliptic curve E-i for i = 1, 2,3 can be written in Legendre form over a cubic extension K of a number field k, then there are infinitely many d is an element of k(x)/(k(x))(2) such that E-i(d)(K) for i = 1, 2, 3 is of positive rank. (C) 2012 Elsevier Inc. All rights reserved
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2013-02
Language
English
Article Type
Article
Keywords

FIELDS

Citation

JOURNAL OF NUMBER THEORY, v.133, no.2, pp.492 - 500

ISSN
0022-314X
DOI
10.1016/j.jnt.2012.08.023
URI
http://hdl.handle.net/10203/212936
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 2 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0