Jacobians of Genus One Curves, Original Research Article

Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P1, a plane cubic, or a space quartic. For each form, a certain syzygy from classical invariant theory gives the curveʹs jacobian in Weierstrass form and the covering map to its jacobian induced by the K-rational divisor at infinity. We give a unified account of all three cases.