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 Gonález-Jiménez and Najman.