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Let $E_i\!: y_i^2 = f(x_i)$ be two copies of a supersingular elliptic curve over a field of odd characteristics. Consider the involution $$ i\!: E_1\times E_2 \to E_1\times E_2,\qquad (x_1, y_1, x_2, y_2) \mapsto (x_2, -y_2, x_1, -y_1) $$ and the quotient $S := E_1\times E_2/i$. Is it a K3 surface? What is (are) its defining equation(s)?

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