Equivariant constrained Willmore tori in the 3-sphere

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In this paper we study equivariant constrained Willmore tori in the 3-sphere. These tori admit a 1-parameter group of Möbius symmetries and are critical points of the Willmore energy under conformal variations. We show that the associated spectral curve of an equivariant torus is given by a double covering of C and classify equivariant constrained Willmore tori by the genus g of their spectral curve. In this case the spectral genus satisfies g ≤ 3.