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When you write QQbar['a'] you get a polynomial ring over QQbar with variable named a, so an elliptic curve over QQbar['a'] must have coefficients polynomial in a.

To use coefficients like 1/a, you can define instead QQbar_a = QQbar['a'].fraction_field().

When you write QQbar['a'] you get a polynomial ring over QQbar with variable named a, so an elliptic curve over QQbar['a'] must have coefficients polynomial in a.

To use coefficients like 1/a, you can define instead QQbar_a = QQbar['a'].fraction_field(), or QQbar_a.<a> = FunctionField(QQbar).