$\operatorname{SU}(2)$-monopoles, curves with symmetries and Ramanujan's heritage

We develop the Ercolani-Sinha construction of SU(2) monopoles for a five-parameter family of centred charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a number-theoretic problem and a recently proven identity of Ramanujan provides a solution.
Bibliography: 36 titles.