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This works:

sage: K.<x, y> = QQ[]
sage: I = Ideal(y^2 - x^3 - x)
sage: L.<X, Y> = K.quotient(I)
sage: I = Ideal(X, Y)
sage: I
Ideal (X, Y) of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (-x^3 + y^2 - x)
sage: X - Y^2 + X^3 in I
True