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).