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Suppose y^2 = x^3+ax+b with a, b ∈ Q defines an elliptic curve. Show that there...

Suppose y^2 = x^3+ax+b with a, b ∈ Q defines an elliptic curve. Show that there is another equation Y^2 = X^3 + AX + B with A, B ∈ Z whose solutions are in bijection with the solutions to y^2 = x^3+ax+b.

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