A minimal generating set for the covariants of the binary cubic consists of the following four covariants: f = a3x³ + 3a₂x²y + 3a₁xy² + aoy3, the form itself; D = azaz - 6a3a0a1a2-3a2a2 + 4a3a0 + 4a2a3, the discriminant; H = (a3a1-a2)x² + (azao-a2a1)yx + (azao-a)y2, the Hessian; and T = (azao-3a3a2a1 +2a2)x³ +(3a3a₁ +3a3a2a0-6a3a)yx²+(-3a₂a + 6azao-3a1azao)y²x + (3a₁azao-2a2-a3a3) y3, the Jacobian of the form and the Hessian. The unique minimal syzygy among these covariants equals f2D - T² - 4H³ = 0.

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