2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107341We 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. The Ercolani-Sinha construction provides a gauge-transform of the Nahm data.65 pages, 6 figuresMathematical PhysicsHigh Energy Physics - TheoryDifferential GeometryExactly Solvable and Integrable Systemstext