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The equation

$$\displaystyle y^2 = f(x_1, x_2, x_3)$$

with $f$ a non-singular quartic form in three variables defines a del Pezzo surface of degree 2. I am interested in the similar construction

$$\displaystyle y^2 = f_1(x_1, x_2, x_3) f_2(x_1, x_2, x_3)$$

where $f_1, f_2$ are quadratic forms defined over $\mathbb{Q}$. Is there anything known about the study of rational points for such surfaces in the weighted projective space $\mathbb{P}(1,1,1,2)$?

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    $\begingroup$ The fibre product of the quadric surfaces $y_i^2=f_i(x_1,x_2,x_3)$ over $\mathbb{P}^2$ (given by co-ordinates $(x_1,x_2,x_3)$) maps to your surface. So perhaps that says something? $\endgroup$
    – Kapil
    Commented Oct 21, 2018 at 2:01
  • $\begingroup$ math.stackexchange.com/questions/1127654/… $\endgroup$
    – individ
    Commented Oct 21, 2018 at 5:08

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