python - How to find minimum y coordinate for elliptical curve y^2 = x^3 + -


How to get the minimum y coordination for a finite field on 
  maximum time = 120960000 p = 976324781263478623476912346213469128736427364a = 783468734639429b = 98347874287423E = alptectak (gf (p), [a, b]) length = 50 In the category I (1, maximum time): E = ZZ.random_element (99 99 99 99 99 99) If E. I_x_corder (i) == true: temp = E.lift_x (i) break i = 0 print 'p1:' print temporary length = 0 t = 50 count = 2 p2 = floating + temporary when calculating & lt; 10000000000: calculation = count + 1 p2 = p2 + temporary if (p2 [1]> gt: if (zz (p2 [1]) & ltzz (p -1): if (p2 [ 0] & gt; 0): If (ZZ (P2 [0]) Lt; ZZ (P-1): If E.Is_X_Corder (P2 [0]) == True: y2 = E.lift_x (P 2 [0]) Length = LAN (Str (y2 [1]) If length & lt; = 11: print 'p2:' print y2 print 'count:' print count if t & gt; length: t = length print 'Length: Print Print' Count: Print Print Print 'P2:' Print Print 2 Print ':'   
 The above stated The sample code with random number is a suggestion or a completely different idea would also be very helpful.  
 Thanks a lot JS   
 
 
 There is no natural order on the elements of GF (P). At least until y, I think you mean by normal order at the integer here p = 17, a = 11, b An example with = 3 is solution y = 3, x = 4.  
  sage: k = gf (17) sage: a, b = 11, 3 sage: _. & Lt; X> = K [] Sage: P = x ^ 3 + one * x + b Procedure: Next ((p - y ^ 2) y if .roots (), y) (p - y ^ 2). ()) ([(4, 1)], 3) Sage: 3 ^ 2 == P (4) Truth   
 Be careful that your  p  is not Is the principal

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