A birdcage resonator for magnetic resonance applications has two ferrules disposed in spaced-apart parallel ferrule planes. A line connecting the ferrule centers defines the antenna axis of the birdcage resonator, which orthogonally intersects the ferrule planes. The birdcage resonator has a number of antenna rods regularly distributed around the antenna axis, extending from ferrule to ferrule. The birdcage resonator has two coupling rings in addition to the ferrules that surround the antenna axis in respective coupling ring planes orthogonal to the antenna axis, and that are spaced from but coupling with the ferrules. The coupling rings are tuned to cause the ferrules to be resonant at frequencies other than without the coupling rings. The ferrules couple with one another in common eigenmodes, namely a common mode with a common mode frequency, and a push-pull mode with a push-pull frequency differing from the common mode frequency. The coupling rings are tuned such that the frequency of one of the eigenmodes does not correspond with any resonance frequency of the antenna rods. A feed device feeds electrical energy into the ferrules at the frequency of the eigenmode that corresponds with no resonance frequency of the antenna rods.