theorem Th60: :: EC_PF_1:60

for p being Prime
for a, b being Element of (GF p) st p > 3 & Disc (a,b,p) <> 0. (GF p) holds
ex F being FinSequence of NAT st
( len F = p & ( for n being Nat st n in Seg p holds
ex d being Element of (GF p) st
( d = n - 1 & F . n = 1 + (Lege_p (((d |^ 3) + (a * d)) + b)) ) ) & card { (Class ((R_EllCur (a,b,p)),P)) where P is Element of ProjCo (GF p) : ( P in EC_SetProjCo (a,b,p) & ex X, Y being Element of (GF p) st P = [X,Y,1] ) } = Sum F )