Growth of torsion groups of elliptic curves over number fields without rationally defined CM

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For a quadratic field K without rationally defined complex multiplication, we prove that there exists of a prime pK depending only on K such that if d is a positive integer whose minimal prime divisor is greater than pK, then for any extension L/K of degree d and any elliptic curve E/K, we have E (L)tors = E (K)tors. By not assuming the GRH, this is a generalization of the results by Genao, and Gonalez-Jimenez and Najman. (c) 2023 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2024-05
Language
English
Article Type
Article
Citation

JOURNAL OF NUMBER THEORY, v.258, pp.1 - 21

ISSN
0022-314X
DOI
10.1016/j.jnt.2023.11.014
URI
http://hdl.handle.net/10203/317985
Appears in Collection
MA-Journal Papers(저널논문)
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