2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123319We study the elliptic modular surface attached to the commutator subgroup of the modular group. This has an elliptic curve as base and only one singular fibre. We employ an algebraic approach and then consider some arithmetic questions.12 pages; dedicated to Michel Raynaud; v2: added Prop. 5 and Section 7Algebraic GeometryNumber Theory14G35, 14J27An interesting elliptic surface over an elliptic curvetext