Euclid Quick Data Release (Q1). The Strong Lensing Discovery Engine A -- System overview and lens catalogue

We present a catalogue of 497 galaxy-galaxy strong lenses in the Euclid Quick Release 1 data (63 deg2$). In the initial 0.45% of Euclid's surveys, we double the total number of known lens candidates with space-based imaging. Our catalogue includes 250 grade A candidates, the vast majority of which (243) were previously unpublished. Euclid's resolution reveals rare lens configurations of scientific value, including double-source-plane lenses, edge-on lenses, complete Einstein rings, and quadruply imaged lenses. We resolve lenses with small Einstein radii ($ < ) in large numbers for the first time. These lenses were found through an initial sweep by deep learning models followed by Space Warps citizen scientist inspection, expert vetting, and system-by-system modelling. Our search approach scales straightforwardly to Euclid Data Release 1 and, without changes, would yield approximately high-confidence (grade A or B) lens candidates by late 2026. Further extrapolating to the complete Euclid Wide Survey implies a likely yield of over high-confidence candidates, transforming strong lensing science. ̊m E ;;1 7000 100000