Quadratic twist of an elliptic curve
= Quadratic twist of an elliptic curve
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For an elliptic curve $E:y^2=f(x)$ over a field of characteristic other than two and $d\in K^\times$, the curve $E^{(d)}:dy^2=f(x)$ is its quadratic twist by $d$. It becomes isomorphic to $E$ after adjoining $\sqrt d$; over a finite field its Frobenius trace is multiplied by the quadratic character of $d$.
= Quadratic twist
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