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.
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