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

Question:

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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