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

Abstract

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.