Jacobians of genus one curves

Consider it curve of genus one over a field K in one of three explicit form s: a double cover of P-1, a plane cubic, or a space quartic. For each form, a certain syzygy from classical invariant theory gibes the curve's jacobia n 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 . (C) 2001 Academic Press.