Consider an elliptic curve $E: y^{2} = x^{3} + ax + b$. Then the quadratic twist by a squarefree $d$ is given by $E^{d} : dy^{2} = x^{3} + ax + b$. What is the relationship between the conductor of $E^{d}$ and $E$?
Relation involving the conductor of an elliptic curve
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number-theory
elliptic-curves