Consider the elliptic curve (mathrm{E}_{11}(1,6)); that is, the curve is defined by (y^{2}=x^{3}+x+6) with a modulus of

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Consider the elliptic curve \(\mathrm{E}_{11}(1,6)\); that is, the curve is defined by \(y^{2}=x^{3}+x+6\) with a modulus of \(p=11\). Determine all of the points in \(\mathrm{E}_{11}(1,6)\). Hint: Start by calculating the right-hand side of the equation for all values of \(x\).

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