We determine the most general time-independent Noether symmetries of twofield cosmological models with rotationally-invariant scalar manifold metrics. In particular, we show that such models can have hidden symmetries, which arise if and only if the scalar manifold metric has Gaussian curvature −3/8, i.e. when the model is of elementary αattractor type with a fixed value of the parameter α. In this case, we find explicitly all scalar potentials compatible with hidden Noether symmetries, thus

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... ssifying all models of this type. We also discuss some implications of the corresponding conserved quantity.