An elliptic curve y = x +ax +8 (mod 31) includes the point P = (8,6)....

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An elliptic curve y = x +ax +8 (mod 31) includes the point P = (8,6). (a) Given that a Z31, determine with justification the value of a. (b) Determine with justification all values of y = Z31 for which there is no point (x, y) on the curve. An elliptic curve y = x +ax +8 (mod 31) includes the point P = (8,6). (a) Given that a Z31, determine with justification the value of a. (b) Determine with justification all values of y = Z31 for which there is no point (x, y) on the curve.