2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128130We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective 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.Rewritten version of math-ph/0601040Mathematical Physicstext