Two-descent on an elliptic curve
= Two-descent on an elliptic curve
When an elliptic curve has full rational <2-torsion>, its Kummer map embeds $E(\mathbb Q)/2E(\mathbb Q)$ into a product of square-class groups. Valuation and local-solubility conditions reduce the image to finitely many classes and thereby bound the rank of the <Mordell-Weil group>.