Torsion and twists of abelian varieties

In this article, we investigate the possible torsion subgroups of twists of abelian varieties with good reduction. As an application, we prove a theorem concerning ramified primes over any quadratic extension where odd‐order torsion growth is achieved. In particular, we show that for every rational elliptic curve and every imaginary quadratic field not equal to satisfying the Heegner hypothesis, no odd‐order torsion growth can occur.