Solving system of polynomial equations over rationals

I want to solve a system of polynomial equations but I need only rational solutions. What is the best method to do it in Sage? For example: Input: R. = QQ[] J = R.ideal(5*(9 + 2*a1^2 - b2), 5*(-324 + 4*a1*b1 + b2^2 - c2), 10*(729 + 2*a1 + b1^2 + 243*b2 - 9*b2^2 + 2*a1*c1 + b2*c2), 5*(6561 + 4*b1 - 2916*b2 + 4*b1*c1 + 486*c2 - 36*b2*c2 + c2^2), 2*(-59048 + 10*c1 + 5*c1^2 - 7290*c2 - 45*c2^2)) J.variety() Output: [] Or example with some solutions (same as above but added constant 1889566 to last equation): Input: R. = QQ[] J = R.ideal(5*(9 + 2*a1^2 - b2), 5*(-324 + 4*a1*b1 + b2^2 - c2), 10*(729 + 2*a1 + b1^2 + 243*b2 - 9*b2^2 + 2*a1*c1 + b2*c2), 5*(6561 + 4*b1 - 2916*b2 + 4*b1*c1 + 486*c2 - 36*b2*c2 + c2^2), 2*(-59048 + 10*c1 + 5*c1^2 - 7290*c2 - 45*c2^2)+1889566) J.variety() Output: [{a1: 0, c1: 0, b1: 0, b2: 9, c2: -243}, {a1: 0, c1: -2, b1: 0, b2: 9, c2: -243}] > **It takes quite a lot of time for the output to appear, while in Mathematica > it takes a second. So is there a > better method in Sage than the one I > used?**