Isogeny Degrees -- Sage

F.<a> = NumberField(x^2-x-1)

PrimeList = [F.ideal(2), F.ideal(3),F.ideal(2*a - 1), F.ideal(7), F.ideal(3*a - 2), F.ideal(3*a - 1),F.ideal(-4*a + 1), F.ideal(-4*a + 3), F.ideal(-a + 6), F.ideal(a + 5), F.ideal(5*a - 2), F.ideal(5*a - 3),F.ideal(a - 7), F.ideal(a + 6), F.ideal(7*a - 2), F.ideal (7*a - 5), F.ideal (7*a - 3),F.ideal(7*a - 4), F.ideal(a - 9), F.ideal(a + 8), F.ideal(-8*a + 5), F.ideal(-8*a + 3),F.ideal(a - 10), F.ideal(a + 9)]

Norms = [P.norm() for P in PrimeList]

len(PrimeList)

f = '/Users/aly/Desktop/ellcurve_aplists.txt' F = file(f,'r') for i in range(7): F.readline()

'#######################################################################\
############\n'
'# A table of elliptic curve eigenforms with norm conductor almost up to
20000.\n'
'# This need not be comprehensive.  There were several levels where the
runs failed.\n'
'# So, if there is nothing for a level in this file, it does not mean
there is no curve.\n'
'#  2010-11-13, William Stein\n'
'#######################################################################\
############\n'
'# Norm    Cond    Number  a2 a3 a5 a7 a11 a11 ...\n'

'###################################################################################\n'
'# A table of elliptic curve eigenforms with norm conductor almost up to 20000.\n'
'# This need not be comprehensive.  There were several levels where the runs failed.\n'
'# So, if there is nothing for a level in this file, it does not mean there is no curve.\n'
'#  2010-11-13, William Stein\n'
'###################################################################################\n'
'# Norm    Cond    Number  a2 a3 a5 a7 a11 a11 ...\n'

R.<x> = ZZ[] Potential_primes1 = [] i = 1 while i > 0: try: Fline = F.readline() Fstgs = Fline.split() aplist = aplist_from_data(Fline) pos = possible_isogeny_degrees(aplist,100) Potential_primes1.append(pos) print Fstgs[0],Fstgs[1], Fstgs[2], pos, aplist i = i + 1 except: i = -1

WARNING: Output truncated!  
full_output.txt



31 5*a-2 0 [2] [-3, 2, -2, 2, 4, -4, 4, -4, -2, -2, '?', '?', -6, -6,
12, -4, 6, -2, -8, 0, 0, 16, 10, -6]
31 5*a-3 0 [2] [-3, 2, -2, 2, -4, 4, -4, 4, -2, -2, '?', '?', -6, -6,
-4, 12, -2, 6, 0, -8, 16, 0, -6, 10]
36 6 0 [2, 5] ['?', '?', -4, 10, 2, 2, 0, 0, 0, 0, -8, -8, 2, 2, -10,
-10, 2, 2, 12, 12, 0, 0, 10, 10]
41 a+6 0 [7] [-2, -4, -1, -6, -2, 5, 6, -1, 2, 9, -10, 4, '?', '?', -3,
4, 6, -8, -12, 9, -11, -4, -1, -8]
41 a-7 0 [7] [-2, -4, -1, -6, 5, -2, -1, 6, 9, 2, 4, -10, '?', '?', 4,
-3, -8, 6, 9, -12, -4, -11, -8, -1]
45 6*a-3 0 [2] [-3, '?', '?', -14, -4, -4, 4, 4, -2, -2, 0, 0, 10, 10,
-4, -4, -2, -2, -8, -8, 0, 0, -6, -6]
49 7 0 [5] [0, 5, -4, '?', -3, -3, 0, 0, 5, 5, 2, 2, 2, 2, -10, -10, -8,
-8, -8, -8, 5, 5, 0, 0]
55 a+7 0 [2, 3] [-1, -2, '?', 14, '?', '?', 8, -4, -6, 6, 8, -4, -6, 6,
-12, 0, -10, 2, 0, 0, -4, 8, -18, 6]
55 -a+8 0 [2, 3] [-1, -2, '?', 14, '?', '?', -4, 8, 6, -6, -4, 8, 6, -6,
0, -12, 2, -10, 0, 0, 8, -4, 6, -18]
64 8 0 [2] ['?', 2, -2, 10, -4, -4, 4, 4, -2, -2, 0, 0, 2, 2, 12, 12,
-10, -10, 8, 8, -16, -16, -6, -6]
71 a+8 0 [2, 3] [-1, -2, 0, -4, 0, 0, 2, -4, 6, -6, 2, 8, 6, 12, -12, 6,
-4, -10, '?', '?', 14, -4, 6, 18]
71 a-9 0 [2, 3] [-1, -2, 0, -4, 0, 0, -4, 2, -6, 6, 8, 2, 12, 6, 6, -12,
-10, -4, '?', '?', -4, 14, 18, 6]
76 -8*a+2 0 [3] ['?', 1, -3, -4, -6, 3, '?', '?', -6, 3, 5, 5, 6, 6, 6,
-12, 8, 8, -9, 0, -1, -1, 9, 0]
76 -8*a+6 0 [3] ['?', 1, -3, -4, 3, -6, '?', '?', 3, -6, 5, 5, 6, 6,
-12, 6, 8, 8, 0, -9, -1, -1, 0, 9]
76 -8*a+2 1 [5] ['?', -5, 1, 0, 2, -3, '?', '?', -10, 5, -3, 7, 2, 2,
10, 0, 12, -8, 7, -8, 15, 5, -15, 0]
76 -8*a+6 1 [5] ['?', -5, 1, 0, -3, 2, '?', '?', 5, -10, 7, -3, 2, 2, 0,
10, -8, 12, -8, 7, 5, 15, 0, -15]
79 -8*a+3 0 [2] [1, -2, -2, -2, -4, 0, 8, 4, -2, 6, 0, -8, -2, 2, 4, -4,
10, 14, 12, -16, '?', '?', 18, -14]
79 -8*a+5 0 [2] [1, -2, -2, -2, 0, -4, 4, 8, 6, -2, -8, 0, 2, -2, -4, 4,
14, 10, -16, 12, '?', '?', -14, 18]
80 8*a-4 0 [2, 3] ['?', -2, '?', -10, 0, 0, -4, -4, 6, 6, -4, -4, 6, 6,
12, 12, 2, 2, -12, -12, 8, 8, -6, -6]
81 9 0 [2, 3, 5] [-1, '?', 0, 14, 0, 0, -4, -4, 0, 0, 8, 8, 0, 0, 0, 0,
2, 2, 0, 0, -16, -16, 0, 0]
89 a-10 0 [2, 3] [-1, 4, 0, -4, -6, 0, -4, 2, 6, 6, -4, -4, 0, 6, 12, 0,
14, -4, 0, 12, -16, 2, '?', '?']
89 a+9 0 [2, 3] [-1, 4, 0, -4, 0, -6, 2, -4, 6, 6, -4, -4, 6, 0, 0, 12,
-4, 14, 12, 0, 2, -16, '?', '?']
95 2*a-11 0 [2, 3] [-1, -2, '?', 2, 0, 0, '?', '?', -6, 6, -4, 8, -6,
-6, 12, 12, -10, 14, 12, 0, -16, 8, 6, -6]
95 -2*a-9 0 [2, 3] [-1, -2, '?', 2, 0, 0, '?', '?', 6, -6, 8, -4, -6,
-6, 12, 12, 14, -10, 0, 12, 8, -16, -6, 6]
99 9*a-3 0 [2] [1, '?', -2, 2, '?', '?', 4, -4, 6, -2, -8, 8, -6, 2, 12,
12, -2, -2, 8, -8, 16, 8, 2, -14]
99 9*a-6 0 [2] [1, '?', -2, 2, '?', '?', -4, 4, -2, 6, 8, -8, 2, -6, 12,
12, -2, -2, -8, 8, 8, 16, -14, 2]
100 10 0 [3, 5] ['?', -5, '?', -10, -3, -3, 5, 5, 0, 0, 2, 2, -3, -3, 0,
0, 2, 2, 12, 12, -10, -10, 15, 15]
100 10 1 [3, 5] ['?', 5, '?', 10, -3, -3, -5, -5, 0, 0, 2, 2, -3, -3, 0,
0, 2, 2, 12, 12, 10, 10, -15, -15]
116 2*a+10 0 [5] ['?', 0, 1, 5, 2, -3, 0, -5, '?', '?', 7, -8, 12, -3,
0, 0, 12, 2, -8, 7, -10, -5, 0, 15]
116 -2*a+12 0 [7] ['?', -4, -1, 1, 5, -2, -1, -8, '?', '?', 4, -3, -7,
0, 4, 4, 6, -8, 9, 16, -11, 10, -1, -8]
116 2*a+10 1 [7] ['?', -4, -1, 1, -2, 5, -8, -1, '?', '?', -3, 4, 0, -7,
4, 4, -8, 6, 16, 9, 10, -11, -8, -1]
116 -2*a+12 1 [5] ['?', 0, 1, 5, -3, 2, -5, 0, '?', '?', -8, 7, -3, 12,
0, 0, 2, 12, 7, -8, -5, -10, 15, 0]
121 11 0 [5] [0, -5, 1, -10, '?', '?', 0, 0, 0, 0, 7, 7, -8, -8, 5, 5,
12, 12, -3, -3, -10, -10, 15, 15]
124 10*a-4 0 [2, 3] ['?', -2, 0, 14, -6, 0, 2, 2, 6, 0, '?', '?', -6, 6,
-12, 0, 8, -10, 0, -12, 8, 8, -6, 6]
124 10*a-6 0 [2, 3] ['?', -2, 0, 14, 0, -6, 2, 2, 0, 6, '?', '?', 6, -6,
0, -12, -10, 8, -12, 0, 8, 8, 6, -6]
124 10*a-4 1 [2] ['?', 2, -2, 2, 4, -4, 4, -4, -2, -2, '?', '?', -6, -6,
12, -4, 6, -2, -8, 0, 0, 16, 10, -6]
124 10*a-6 1 [2] ['?', 2, -2, 2, -4, 4, -4, 4, -2, -2, '?', '?', -6, -6,
-4, 12, -2, 6, 0, -8, 16, 0, -6, 10]
144 12 0 [2] ['?', '?', 2, -2, -4, -4, 0, 0, 6, 6, 4, 4, -10, -10, -4,
-4, 2, 2, 0, 0, 12, 12, 10, 10]
144 12 1 [2, 5] ['?', '?', -4, 10, 2, 2, 0, 0, 0, 0, -8, -8, 2, 2, -10,
-10, 2, 2, 12, 12, 0, 0, 10, 10]
145 11*a-3 0 [2] [1, -6, '?', 2, 4, -4, -4, 4, '?', '?', 8, 0, -6, 10,
-12, 4, -2, -2, -16, 0, 16, 8, 10, -6]
145 11*a-8 0 [7] [-2, 3, '?', 8, 5, -2, -8, -1, '?', '?', -3, -10, 7, 0,
4, -3, -8, 13, -12, 2, -4, 10, 6, 13]
145 11*a-3 1 [7] [-2, 3, '?', 8, -2, 5, -1, -8, '?', '?', -10, -3, 0, 7,
-3, 4, 13, -8, 2, -12, 10, -4, 13, 6]
145 11*a-8 1 [3] [2, 1, '?', -4, -3, -6, -4, 5, '?', '?', 5, 2, -9, 0,
12, -9, -4, 5, 12, -6, -4, 2, -6, 15]
145 11*a-3 2 [3] [2, 1, '?', -4, -6, -3, 5, -4, '?', '?', 2, 5, 0, -9,
-9, 12, 5, -4, -6, 12, 2, -4, 15, -6]
145 11*a-8 2 [2] [1, -6, '?', 2, -4, 4, 4, -4, '?', '?', 0, 8, 10, -6,
4, -12, -2, -2, 0, -16, 8, 16, -6, 10]
155 a+12 0 [2] [1, -2, '?', -6, 0, 4, -4, 0, -2, -2, '?', '?', 2, 2,
-12, 12, 10, -2, 16, -4, -8, 16, 18, 10]
155 a-13 0 [2] [1, -2, '?', -6, 4, 0, 0, -4, -2, -2, '?', '?', 2, 2, 12,
-12, -2, 10, -4, 16, 16, -8, 10, 18]
155 a+12 1 [2] [-3, 2, '?', 2, 4, -4, 4, -4, -2, -2, '?', '?', -6, -6,
12, -4, 6, -2, -8, 0, 0, 16, 10, -6]
155 a-13 1 [2] [-3, 2, '?', 2, -4, 4, -4, 4, -2, -2, '?', '?', -6, -6,
-4, 12, -2, 6, 0, -8, 16, 0, -6, 10]
164 2*a+12 0 [2] ['?', 2, 2, -6, -2, -4, -6, 8, 8, -6, -4, -8, '?', '?',
0, 4, 0, -8, 0, 0, 16, -4, 14, 10]
164 2*a-14 0 [2] ['?', 2, 2, -6, -4, -2, 8, -6, -6, 8, -8, -4, '?', '?',
4, 0, -8, 0, 0, 0, -4, 16, 10, 14]
164 2*a+12 1 [7] ['?', -4, -1, -6, -2, 5, 6, -1, 2, 9, -10, 4, '?', '?',
-3, 4, 6, -8, -12, 9, -11, -4, -1, -8]
164 2*a-14 1 [7] ['?', -4, -1, -6, 5, -2, -1, 6, 9, 2, 4, -10, '?', '?',
4, -3, -8, 6, 9, -12, -4, -11, -8, -1]
171 -12*a+3 0 [2, 3] [-1, '?', 0, -10, 6, 0, '?', '?', -6, 0, -4, -4,
-6, 12, -6, 6, 2, 14, -6, 6, -4, 8, 6, 12]
171 -12*a+9 0 [2, 3] [-1, '?', 0, -10, 0, 6, '?', '?', 0, -6, -4, -4,
12, -6, 6, -6, 14, 2, 6, -6, 8, -4, 12, 6]
176 12*a-4 0 [2, 3] ['?', -2, 0, 8, '?', '?', -4, 2, -6, -6, -4, 2, -6,
0, 0, 12, -10, 8, 0, 12, 8, -10, 6, 6]
176 12*a-8 0 [2, 3] ['?', -2, 0, 8, '?', '?', 2, -4, -6, -6, 2, -4, 0,
-6, 12, 0, 8, -10, 12, 0, -10, 8, 6, 6]
179 -12*a+5 0 [] [1, 0, 0, -5, 3, -5, -4, 1, 5, 7, 1, 2, -3, -6, -4, 8,
-11, -10, 10, 12, 0, 12, 4, 4]
179 12*a-7 0 [] [1, 0, 0, -5, -5, 3, 1, -4, 7, 5, 2, 1, -6, -3, 8, -4,
-10, -11, 12, 10, 12, 0, 4, 4]

...

19844 126*a-64 20 [2] ['?', 4, -2, -10, '?', '?', 6, 4, 0, 2, 4, -10,
'?', '?', 4, 0, -4, -14, 2, -8, -8, 14, 10, 12]
19844 -16*a-134 20 [7] ['?', -4, -1, -6, '?', '?', -1, 6, 9, 2, 4, -10,
'?', '?', 4, -3, -8, 6, 9, -12, -4, -11, -8, -1]
19844 126*a-62 21 [2] ['?', 2, 2, -6, '?', '?', 8, -6, -6, 8, -8, -4,
'?', '?', 4, 0, -8, 0, 0, 0, -4, 16, 10, 14]
19844 126*a-64 21 [2] ['?', 2, 2, -6, '?', '?', -6, 8, 8, -6, -4, -8,
'?', '?', 0, 4, 0, -8, 0, 0, 16, -4, 14, 10]
19844 -16*a-134 21 [] ['?', -1, 3, 0, '?', '?', -2, 3, 10, 6, 0, 8, '?',
'?', 7, -6, -13, 6, 6, 4, -11, 10, 7, -12]
19844 126*a-62 22 [2] ['?', 4, 2, 10, '?', '?', -4, 6, 2, 0, 10, -4,
'?', '?', 0, 4, 14, -4, -8, 2, -14, -8, -12, -10]
19844 126*a-64 22 [2] ['?', 4, 2, 10, '?', '?', 6, -4, 0, 2, -4, 10,
'?', '?', 4, 0, -4, 14, 2, -8, -8, -14, -10, -12]
19844 126*a-62 23 [3] ['?', 1, 3, -5, '?', '?', -2, 8, 9, -3, 4, -2,
'?', '?', -6, 0, 1, -1, 0, 6, -8, -10, 3, 18]
19844 126*a-64 23 [3] ['?', 1, 3, -5, '?', '?', 8, -2, -3, 9, -2, 4,
'?', '?', 0, -6, -1, 1, 6, 0, -10, -8, 18, 3]
19844 126*a-62 24 [3] ['?', -2, 3, 13, '?', '?', 7, -1, 0, 0, 7, 1, '?',
'?', 0, -12, -8, -10, -3, 6, -5, 11, 15, 6]
19844 126*a-64 24 [3] ['?', -2, 3, 13, '?', '?', -1, 7, 0, 0, 1, 7, '?',
'?', -12, 0, -10, -8, 6, -3, 11, -5, 6, 15]
19844 126*a-62 25 [] ['?', -1, -1, -5, '?', '?', 4, 4, -3, 7, 2, 0, '?',
'?', 0, 0, 1, 5, 2, 6, 8, -6, 5, 6]
19844 126*a-64 25 [] ['?', -1, -1, -5, '?', '?', 4, 4, 7, -3, 0, 2, '?',
'?', 0, 0, 5, 1, 6, 2, -6, 8, 6, 5]
19844 126*a-62 26 [7] ['?', -4, -1, -6, '?', '?', -1, 6, 9, 2, 4, -10,
'?', '?', 4, -3, -8, 6, 9, -12, -4, -11, -8, -1]
19844 126*a-64 26 [7] ['?', -4, -1, -6, '?', '?', 6, -1, 2, 9, -10, 4,
'?', '?', -3, 4, 6, -8, -12, 9, -11, -4, -1, -8]
19844 126*a-62 27 [] ['?', 1, -1, -5, '?', '?', 2, 0, 5, 9, 4, 2, '?',
'?', 6, -8, 5, -13, -8, 2, -8, 10, 3, 2]
19844 126*a-64 27 [] ['?', 1, -1, -5, '?', '?', 0, 2, 9, 5, 2, 4, '?',
'?', -8, 6, -13, 5, 2, -8, 10, -8, 2, 3]
19845 126*a-63 0 [2] [3, '?', '?', '?', -2, 4, -2, 4, 8, -4, 0, 6, 2, 2,
4, 4, -8, 4, 8, -10, 0, 0, 6, -18]
19845 126*a-63 1 [2] [-3, '?', '?', '?', 4, 4, 4, 4, -2, -2, 0, 0, 2, 2,
12, 12, -2, -2, 0, 0, -16, -16, -14, -14]
19845 126*a-63 2 [2, 3] [-1, '?', '?', '?', 6, 0, 8, 2, -6, 6, -10, 8,
-6, 6, -12, 0, -4, 8, 12, 6, 8, -4, 6, 6]
19845 126*a-63 3 [2] [3, '?', '?', '?', 0, 0, 0, 0, 8, 8, -4, -4, -4,
-4, 8, 8, 10, 10, 16, 16, 8, 8, -12, -12]
19845 126*a-63 4 [2] [-3, '?', '?', '?', -4, -4, 4, 4, -2, -2, 0, 0, 10,
10, -4, -4, -2, -2, -8, -8, 0, 0, -6, -6]
19845 126*a-63 5 [2] [3, '?', '?', '?', 6, 6, 6, 6, -2, -2, -10, -10,
-2, -2, -8, -8, -2, -2, -10, -10, -4, -4, 6, 6]
19845 126*a-63 6 [2] [1, '?', '?', '?', 4, -4, 0, -8, 10, -6, -4, 4, -6,
-6, -12, 4, -10, 6, 8, 0, 8, -8, -6, -6]
19845 126*a-63 7 [3] [-4, '?', '?', '?', 3, 3, 2, 2, -3, -3, -4, -4, 12,
12, 0, 0, 8, 8, 0, 0, -1, -1, 12, 12]
19845 126*a-63 8 [2] [-3, '?', '?', '?', -4, -4, 4, 4, 2, 2, 0, 0, -2,
-2, -12, -12, -2, -2, 0, 0, -16, -16, 14, 14]
19845 126*a-63 9 [2] [3, '?', '?', '?', 2, -4, -2, 4, -8, 4, 0, 6, -2,
-2, -4, -4, -8, 4, -8, 10, 0, 0, -6, 18]
19845 126*a-63 10 [2] [-1, '?', '?', '?', 6, -2, -2, -2, 6, 6, -2, -2,
-6, 10, 0, 0, 14, -2, -10, -2, 4, -12, 10, 10]
19845 126*a-63 11 [2] [-1, '?', '?', '?', -2, 6, -2, -2, 6, 6, -2, -2,
10, -6, 0, 0, -2, 14, -2, -10, -12, 4, 10, 10]
19845 126*a-63 12 [2] [-1, '?', '?', '?', 2, 0, -6, 4, 8, -4, -8, -6, 6,
-2, -4, -4, -4, 0, -12, 10, -8, 8, -6, 2]
19845 126*a-63 13 [2] [-3, '?', '?', '?', 0, 0, -8, -8, -2, -2, 4, 4,
-6, -6, 4, 4, -2, -2, -12, -12, 8, 8, -6, -6]
19845 126*a-63 14 [2] [-1, '?', '?', '?', -6, 2, -2, -2, -6, -6, -2, -2,
6, -10, 0, 0, 14, -2, 10, 2, 4, -12, -10, -10]
19845 126*a-63 15 [2] [-1, '?', '?', '?', 2, -6, -2, -2, -6, -6, -2, -2,
-10, 6, 0, 0, -2, 14, 2, 10, -12, 4, -10, -10]
19845 126*a-63 16 [2] [-1, '?', '?', '?', 0, -2, 4, -6, 4, -8, -6, -8,
2, -6, 4, 4, 0, -4, -10, 12, 8, -8, -2, 6]
19845 126*a-63 17 [2] [-1, '?', '?', '?', -2, 0, -6, 4, -8, 4, -8, -6,
-6, 2, 4, 4, -4, 0, 12, -10, -8, 8, 6, -2]
19845 126*a-63 18 [2] [-1, '?', '?', '?', 0, 2, 4, -6, -4, 8, -6, -8,
-2, 6, -4, -4, 0, -4, 10, -12, 8, -8, 2, -6]
19845 126*a-63 19 [2, 3] [-1, '?', '?', '?', -6, 0, 8, 2, 6, -6, -10, 8,
6, -6, 12, 0, -4, 8, -12, -6, 8, -4, -6, -6]
19845 126*a-63 20 [2, 3] [-1, '?', '?', '?', 0, -6, 2, 8, -6, 6, 8, -10,
-6, 6, 0, 12, 8, -4, -6, -12, -4, 8, -6, -6]
19845 126*a-63 21 [2] [-3, '?', '?', '?', 0, 0, -8, -8, 2, 2, 4, 4, 6,
6, -4, -4, -2, -2, 12, 12, 8, 8, 6, 6]
19845 126*a-63 22 [2] [3, '?', '?', '?', -4, 2, 4, -2, 4, -8, 6, 0, -2,
-2, -4, -4, 4, -8, 10, -8, 0, 0, 18, -6]
19845 126*a-63 23 [2] [3, '?', '?', '?', 0, 0, 0, 0, -8, -8, -4, -4, 4,
4, -8, -8, 10, 10, -16, -16, 8, 8, 12, 12]
19845 126*a-63 24 [2] [3, '?', '?', '?', -6, -6, 6, 6, 2, 2, -10, -10,
2, 2, 8, 8, -2, -2, 10, 10, -4, -4, -6, -6]
19845 126*a-63 25 [2] [-3, '?', '?', '?', 4, 4, 4, 4, 2, 2, 0, 0, -10,
-10, 4, 4, -2, -2, 8, 8, 0, 0, 6, 6]
19845 126*a-63 26 [5] [0, '?', '?', '?', 3, 3, 0, 0, -5, -5, 2, 2, -2,
-2, 10, 10, -8, -8, 8, 8, 5, 5, 0, 0]
19845 126*a-63 27 [2] [1, '?', '?', '?', -4, 4, -8, 0, -6, 10, 4, -4,
-6, -6, 4, -12, 6, -10, 0, 8, -8, 8, -6, -6]
19845 126*a-63 28 [2, 3] [-1, '?', '?', '?', 0, 6, 2, 8, 6, -6, 8, -10,
6, -6, 0, -12, 8, -4, 6, 12, -4, 8, 6, 6]
19845 126*a-63 29 [2, 3, 5] [-1, '?', '?', '?', 0, 0, -4, -4, 0, 0, 8,
8, 0, 0, 0, 0, 2, 2, 0, 0, -16, -16, 0, 0]
19845 126*a-63 30 [5] [0, '?', '?', '?', -3, -3, 0, 0, 5, 5, 2, 2, 2, 2,
-10, -10, -8, -8, -8, -8, 5, 5, 0, 0]
19845 126*a-63 31 [2] [1, '?', '?', '?', -4, 4, 0, -8, -10, 6, -4, 4, 6,
6, 12, -4, -10, 6, -8, 0, 8, -8, 6, 6]
19845 126*a-63 32 [2] [1, '?', '?', '?', 4, -4, -8, 0, 6, -10, 4, -4, 6,
6, -4, 12, 6, -10, 0, -8, -8, 8, 6, 6]
19845 126*a-63 33 [3] [-4, '?', '?', '?', -3, -3, 2, 2, 3, 3, -4, -4,
-12, -12, 0, 0, 8, 8, 0, 0, -1, -1, -12, -12]
19845 126*a-63 34 [2] [3, '?', '?', '?', 4, -2, 4, -2, -4, 8, 6, 0, 2,
2, 4, 4, 4, -8, -10, 8, 0, 0, -18, 6]
19871 -11*a-136 0 [] [-1, -1, -2, 8, -2, -5, 1, -3, 0, -3, '?', '?', -3,
-6, -3, 0, 0, -2, -6, -1, -4, 6, -9, 1]
19871 -129*a+95 0 [] [-1, -1, -2, 8, -2, -5, 1, -3, 0, -3, '?', '?', -3,
-6, -3, 0, 0, -2, -6, -1, -4, 6, -9, 1]
19871 -11*a-136 1 [] [2, 4, 2, -5, -3, -5, 1, -2, 6, 9, '?', '?', -6,
-5, 14, -8, 15, -10, 6, -10, 13, 8, 5, -9]
19871 -129*a+95 1 [] [2, 4, -2, 3, 3, 3, 3, 2, 10, 3, '?', '?', 0, -9,
6, 10, -3, 0, 0, -6, -1, 8, -9, 3]
19871 -11*a-136 2 [2] [1, 4, -2, -6, 0, 2, -6, 4, 8, -2, '?', '?', -10,
-10, -12, -4, -6, -8, 12, -8, -8, 2, -10, -14]
19871 -129*a+95 2 [2] [-3, 2, -2, 2, 4, -4, 4, -4, -2, -2, '?', '?', -6,
-6, 12, -4, 6, -2, -8, 0, 0, 16, 10, -6]
19871 -11*a-136 3 [2] [-3, 2, -2, 2, -4, 4, -4, 4, -2, -2, '?', '?', -6,
-6, -4, 12, -2, 6, 0, -8, 16, 0, -6, 10]
19871 -129*a+95 3 [] [2, 4, 2, -5, -3, -5, 1, -2, 6, 9, '?', '?', -6,
-5, 14, -8, 15, -10, 6, -10, 13, 8, 5, -9]

WARNING: Output truncated!  
full_output.txt



31 5*a-2 0 [2] [-3, 2, -2, 2, 4, -4, 4, -4, -2, -2, '?', '?', -6, -6, 12, -4, 6, -2, -8, 0, 0, 16, 10, -6]
31 5*a-3 0 [2] [-3, 2, -2, 2, -4, 4, -4, 4, -2, -2, '?', '?', -6, -6, -4, 12, -2, 6, 0, -8, 16, 0, -6, 10]
36 6 0 [2, 5] ['?', '?', -4, 10, 2, 2, 0, 0, 0, 0, -8, -8, 2, 2, -10, -10, 2, 2, 12, 12, 0, 0, 10, 10]
41 a+6 0 [7] [-2, -4, -1, -6, -2, 5, 6, -1, 2, 9, -10, 4, '?', '?', -3, 4, 6, -8, -12, 9, -11, -4, -1, -8]
41 a-7 0 [7] [-2, -4, -1, -6, 5, -2, -1, 6, 9, 2, 4, -10, '?', '?', 4, -3, -8, 6, 9, -12, -4, -11, -8, -1]
45 6*a-3 0 [2] [-3, '?', '?', -14, -4, -4, 4, 4, -2, -2, 0, 0, 10, 10, -4, -4, -2, -2, -8, -8, 0, 0, -6, -6]
49 7 0 [5] [0, 5, -4, '?', -3, -3, 0, 0, 5, 5, 2, 2, 2, 2, -10, -10, -8, -8, -8, -8, 5, 5, 0, 0]
55 a+7 0 [2, 3] [-1, -2, '?', 14, '?', '?', 8, -4, -6, 6, 8, -4, -6, 6, -12, 0, -10, 2, 0, 0, -4, 8, -18, 6]
55 -a+8 0 [2, 3] [-1, -2, '?', 14, '?', '?', -4, 8, 6, -6, -4, 8, 6, -6, 0, -12, 2, -10, 0, 0, 8, -4, 6, -18]
64 8 0 [2] ['?', 2, -2, 10, -4, -4, 4, 4, -2, -2, 0, 0, 2, 2, 12, 12, -10, -10, 8, 8, -16, -16, -6, -6]
71 a+8 0 [2, 3] [-1, -2, 0, -4, 0, 0, 2, -4, 6, -6, 2, 8, 6, 12, -12, 6, -4, -10, '?', '?', 14, -4, 6, 18]
71 a-9 0 [2, 3] [-1, -2, 0, -4, 0, 0, -4, 2, -6, 6, 8, 2, 12, 6, 6, -12, -10, -4, '?', '?', -4, 14, 18, 6]
76 -8*a+2 0 [3] ['?', 1, -3, -4, -6, 3, '?', '?', -6, 3, 5, 5, 6, 6, 6, -12, 8, 8, -9, 0, -1, -1, 9, 0]
76 -8*a+6 0 [3] ['?', 1, -3, -4, 3, -6, '?', '?', 3, -6, 5, 5, 6, 6, -12, 6, 8, 8, 0, -9, -1, -1, 0, 9]
76 -8*a+2 1 [5] ['?', -5, 1, 0, 2, -3, '?', '?', -10, 5, -3, 7, 2, 2, 10, 0, 12, -8, 7, -8, 15, 5, -15, 0]
76 -8*a+6 1 [5] ['?', -5, 1, 0, -3, 2, '?', '?', 5, -10, 7, -3, 2, 2, 0, 10, -8, 12, -8, 7, 5, 15, 0, -15]
79 -8*a+3 0 [2] [1, -2, -2, -2, -4, 0, 8, 4, -2, 6, 0, -8, -2, 2, 4, -4, 10, 14, 12, -16, '?', '?', 18, -14]
79 -8*a+5 0 [2] [1, -2, -2, -2, 0, -4, 4, 8, 6, -2, -8, 0, 2, -2, -4, 4, 14, 10, -16, 12, '?', '?', -14, 18]
80 8*a-4 0 [2, 3] ['?', -2, '?', -10, 0, 0, -4, -4, 6, 6, -4, -4, 6, 6, 12, 12, 2, 2, -12, -12, 8, 8, -6, -6]
81 9 0 [2, 3, 5] [-1, '?', 0, 14, 0, 0, -4, -4, 0, 0, 8, 8, 0, 0, 0, 0, 2, 2, 0, 0, -16, -16, 0, 0]
89 a-10 0 [2, 3] [-1, 4, 0, -4, -6, 0, -4, 2, 6, 6, -4, -4, 0, 6, 12, 0, 14, -4, 0, 12, -16, 2, '?', '?']
89 a+9 0 [2, 3] [-1, 4, 0, -4, 0, -6, 2, -4, 6, 6, -4, -4, 6, 0, 0, 12, -4, 14, 12, 0, 2, -16, '?', '?']
95 2*a-11 0 [2, 3] [-1, -2, '?', 2, 0, 0, '?', '?', -6, 6, -4, 8, -6, -6, 12, 12, -10, 14, 12, 0, -16, 8, 6, -6]
95 -2*a-9 0 [2, 3] [-1, -2, '?', 2, 0, 0, '?', '?', 6, -6, 8, -4, -6, -6, 12, 12, 14, -10, 0, 12, 8, -16, -6, 6]
99 9*a-3 0 [2] [1, '?', -2, 2, '?', '?', 4, -4, 6, -2, -8, 8, -6, 2, 12, 12, -2, -2, 8, -8, 16, 8, 2, -14]
99 9*a-6 0 [2] [1, '?', -2, 2, '?', '?', -4, 4, -2, 6, 8, -8, 2, -6, 12, 12, -2, -2, -8, 8, 8, 16, -14, 2]
100 10 0 [3, 5] ['?', -5, '?', -10, -3, -3, 5, 5, 0, 0, 2, 2, -3, -3, 0, 0, 2, 2, 12, 12, -10, -10, 15, 15]
100 10 1 [3, 5] ['?', 5, '?', 10, -3, -3, -5, -5, 0, 0, 2, 2, -3, -3, 0, 0, 2, 2, 12, 12, 10, 10, -15, -15]
116 2*a+10 0 [5] ['?', 0, 1, 5, 2, -3, 0, -5, '?', '?', 7, -8, 12, -3, 0, 0, 12, 2, -8, 7, -10, -5, 0, 15]
116 -2*a+12 0 [7] ['?', -4, -1, 1, 5, -2, -1, -8, '?', '?', 4, -3, -7, 0, 4, 4, 6, -8, 9, 16, -11, 10, -1, -8]
116 2*a+10 1 [7] ['?', -4, -1, 1, -2, 5, -8, -1, '?', '?', -3, 4, 0, -7, 4, 4, -8, 6, 16, 9, 10, -11, -8, -1]
116 -2*a+12 1 [5] ['?', 0, 1, 5, -3, 2, -5, 0, '?', '?', -8, 7, -3, 12, 0, 0, 2, 12, 7, -8, -5, -10, 15, 0]
121 11 0 [5] [0, -5, 1, -10, '?', '?', 0, 0, 0, 0, 7, 7, -8, -8, 5, 5, 12, 12, -3, -3, -10, -10, 15, 15]
124 10*a-4 0 [2, 3] ['?', -2, 0, 14, -6, 0, 2, 2, 6, 0, '?', '?', -6, 6, -12, 0, 8, -10, 0, -12, 8, 8, -6, 6]
124 10*a-6 0 [2, 3] ['?', -2, 0, 14, 0, -6, 2, 2, 0, 6, '?', '?', 6, -6, 0, -12, -10, 8, -12, 0, 8, 8, 6, -6]
124 10*a-4 1 [2] ['?', 2, -2, 2, 4, -4, 4, -4, -2, -2, '?', '?', -6, -6, 12, -4, 6, -2, -8, 0, 0, 16, 10, -6]
124 10*a-6 1 [2] ['?', 2, -2, 2, -4, 4, -4, 4, -2, -2, '?', '?', -6, -6, -4, 12, -2, 6, 0, -8, 16, 0, -6, 10]
144 12 0 [2] ['?', '?', 2, -2, -4, -4, 0, 0, 6, 6, 4, 4, -10, -10, -4, -4, 2, 2, 0, 0, 12, 12, 10, 10]
144 12 1 [2, 5] ['?', '?', -4, 10, 2, 2, 0, 0, 0, 0, -8, -8, 2, 2, -10, -10, 2, 2, 12, 12, 0, 0, 10, 10]
145 11*a-3 0 [2] [1, -6, '?', 2, 4, -4, -4, 4, '?', '?', 8, 0, -6, 10, -12, 4, -2, -2, -16, 0, 16, 8, 10, -6]
145 11*a-8 0 [7] [-2, 3, '?', 8, 5, -2, -8, -1, '?', '?', -3, -10, 7, 0, 4, -3, -8, 13, -12, 2, -4, 10, 6, 13]
145 11*a-3 1 [7] [-2, 3, '?', 8, -2, 5, -1, -8, '?', '?', -10, -3, 0, 7, -3, 4, 13, -8, 2, -12, 10, -4, 13, 6]
145 11*a-8 1 [3] [2, 1, '?', -4, -3, -6, -4, 5, '?', '?', 5, 2, -9, 0, 12, -9, -4, 5, 12, -6, -4, 2, -6, 15]
145 11*a-3 2 [3] [2, 1, '?', -4, -6, -3, 5, -4, '?', '?', 2, 5, 0, -9, -9, 12, 5, -4, -6, 12, 2, -4, 15, -6]
145 11*a-8 2 [2] [1, -6, '?', 2, -4, 4, 4, -4, '?', '?', 0, 8, 10, -6, 4, -12, -2, -2, 0, -16, 8, 16, -6, 10]
155 a+12 0 [2] [1, -2, '?', -6, 0, 4, -4, 0, -2, -2, '?', '?', 2, 2, -12, 12, 10, -2, 16, -4, -8, 16, 18, 10]
155 a-13 0 [2] [1, -2, '?', -6, 4, 0, 0, -4, -2, -2, '?', '?', 2, 2, 12, -12, -2, 10, -4, 16, 16, -8, 10, 18]
155 a+12 1 [2] [-3, 2, '?', 2, 4, -4, 4, -4, -2, -2, '?', '?', -6, -6, 12, -4, 6, -2, -8, 0, 0, 16, 10, -6]
155 a-13 1 [2] [-3, 2, '?', 2, -4, 4, -4, 4, -2, -2, '?', '?', -6, -6, -4, 12, -2, 6, 0, -8, 16, 0, -6, 10]
164 2*a+12 0 [2] ['?', 2, 2, -6, -2, -4, -6, 8, 8, -6, -4, -8, '?', '?', 0, 4, 0, -8, 0, 0, 16, -4, 14, 10]
164 2*a-14 0 [2] ['?', 2, 2, -6, -4, -2, 8, -6, -6, 8, -8, -4, '?', '?', 4, 0, -8, 0, 0, 0, -4, 16, 10, 14]
164 2*a+12 1 [7] ['?', -4, -1, -6, -2, 5, 6, -1, 2, 9, -10, 4, '?', '?', -3, 4, 6, -8, -12, 9, -11, -4, -1, -8]
164 2*a-14 1 [7] ['?', -4, -1, -6, 5, -2, -1, 6, 9, 2, 4, -10, '?', '?', 4, -3, -8, 6, 9, -12, -4, -11, -8, -1]
171 -12*a+3 0 [2, 3] [-1, '?', 0, -10, 6, 0, '?', '?', -6, 0, -4, -4, -6, 12, -6, 6, 2, 14, -6, 6, -4, 8, 6, 12]
171 -12*a+9 0 [2, 3] [-1, '?', 0, -10, 0, 6, '?', '?', 0, -6, -4, -4, 12, -6, 6, -6, 14, 2, 6, -6, 8, -4, 12, 6]
176 12*a-4 0 [2, 3] ['?', -2, 0, 8, '?', '?', -4, 2, -6, -6, -4, 2, -6, 0, 0, 12, -10, 8, 0, 12, 8, -10, 6, 6]
176 12*a-8 0 [2, 3] ['?', -2, 0, 8, '?', '?', 2, -4, -6, -6, 2, -4, 0, -6, 12, 0, 8, -10, 12, 0, -10, 8, 6, 6]
179 -12*a+5 0 [] [1, 0, 0, -5, 3, -5, -4, 1, 5, 7, 1, 2, -3, -6, -4, 8, -11, -10, 10, 12, 0, 12, 4, 4]
179 12*a-7 0 [] [1, 0, 0, -5, -5, 3, 1, -4, 7, 5, 2, 1, -6, -3, 8, -4, -10, -11, 12, 10, 12, 0, 4, 4]

...

19844 126*a-64 20 [2] ['?', 4, -2, -10, '?', '?', 6, 4, 0, 2, 4, -10, '?', '?', 4, 0, -4, -14, 2, -8, -8, 14, 10, 12]
19844 -16*a-134 20 [7] ['?', -4, -1, -6, '?', '?', -1, 6, 9, 2, 4, -10, '?', '?', 4, -3, -8, 6, 9, -12, -4, -11, -8, -1]
19844 126*a-62 21 [2] ['?', 2, 2, -6, '?', '?', 8, -6, -6, 8, -8, -4, '?', '?', 4, 0, -8, 0, 0, 0, -4, 16, 10, 14]
19844 126*a-64 21 [2] ['?', 2, 2, -6, '?', '?', -6, 8, 8, -6, -4, -8, '?', '?', 0, 4, 0, -8, 0, 0, 16, -4, 14, 10]
19844 -16*a-134 21 [] ['?', -1, 3, 0, '?', '?', -2, 3, 10, 6, 0, 8, '?', '?', 7, -6, -13, 6, 6, 4, -11, 10, 7, -12]
19844 126*a-62 22 [2] ['?', 4, 2, 10, '?', '?', -4, 6, 2, 0, 10, -4, '?', '?', 0, 4, 14, -4, -8, 2, -14, -8, -12, -10]
19844 126*a-64 22 [2] ['?', 4, 2, 10, '?', '?', 6, -4, 0, 2, -4, 10, '?', '?', 4, 0, -4, 14, 2, -8, -8, -14, -10, -12]
19844 126*a-62 23 [3] ['?', 1, 3, -5, '?', '?', -2, 8, 9, -3, 4, -2, '?', '?', -6, 0, 1, -1, 0, 6, -8, -10, 3, 18]
19844 126*a-64 23 [3] ['?', 1, 3, -5, '?', '?', 8, -2, -3, 9, -2, 4, '?', '?', 0, -6, -1, 1, 6, 0, -10, -8, 18, 3]
19844 126*a-62 24 [3] ['?', -2, 3, 13, '?', '?', 7, -1, 0, 0, 7, 1, '?', '?', 0, -12, -8, -10, -3, 6, -5, 11, 15, 6]
19844 126*a-64 24 [3] ['?', -2, 3, 13, '?', '?', -1, 7, 0, 0, 1, 7, '?', '?', -12, 0, -10, -8, 6, -3, 11, -5, 6, 15]
19844 126*a-62 25 [] ['?', -1, -1, -5, '?', '?', 4, 4, -3, 7, 2, 0, '?', '?', 0, 0, 1, 5, 2, 6, 8, -6, 5, 6]
19844 126*a-64 25 [] ['?', -1, -1, -5, '?', '?', 4, 4, 7, -3, 0, 2, '?', '?', 0, 0, 5, 1, 6, 2, -6, 8, 6, 5]
19844 126*a-62 26 [7] ['?', -4, -1, -6, '?', '?', -1, 6, 9, 2, 4, -10, '?', '?', 4, -3, -8, 6, 9, -12, -4, -11, -8, -1]
19844 126*a-64 26 [7] ['?', -4, -1, -6, '?', '?', 6, -1, 2, 9, -10, 4, '?', '?', -3, 4, 6, -8, -12, 9, -11, -4, -1, -8]
19844 126*a-62 27 [] ['?', 1, -1, -5, '?', '?', 2, 0, 5, 9, 4, 2, '?', '?', 6, -8, 5, -13, -8, 2, -8, 10, 3, 2]
19844 126*a-64 27 [] ['?', 1, -1, -5, '?', '?', 0, 2, 9, 5, 2, 4, '?', '?', -8, 6, -13, 5, 2, -8, 10, -8, 2, 3]
19845 126*a-63 0 [2] [3, '?', '?', '?', -2, 4, -2, 4, 8, -4, 0, 6, 2, 2, 4, 4, -8, 4, 8, -10, 0, 0, 6, -18]
19845 126*a-63 1 [2] [-3, '?', '?', '?', 4, 4, 4, 4, -2, -2, 0, 0, 2, 2, 12, 12, -2, -2, 0, 0, -16, -16, -14, -14]
19845 126*a-63 2 [2, 3] [-1, '?', '?', '?', 6, 0, 8, 2, -6, 6, -10, 8, -6, 6, -12, 0, -4, 8, 12, 6, 8, -4, 6, 6]
19845 126*a-63 3 [2] [3, '?', '?', '?', 0, 0, 0, 0, 8, 8, -4, -4, -4, -4, 8, 8, 10, 10, 16, 16, 8, 8, -12, -12]
19845 126*a-63 4 [2] [-3, '?', '?', '?', -4, -4, 4, 4, -2, -2, 0, 0, 10, 10, -4, -4, -2, -2, -8, -8, 0, 0, -6, -6]
19845 126*a-63 5 [2] [3, '?', '?', '?', 6, 6, 6, 6, -2, -2, -10, -10, -2, -2, -8, -8, -2, -2, -10, -10, -4, -4, 6, 6]
19845 126*a-63 6 [2] [1, '?', '?', '?', 4, -4, 0, -8, 10, -6, -4, 4, -6, -6, -12, 4, -10, 6, 8, 0, 8, -8, -6, -6]
19845 126*a-63 7 [3] [-4, '?', '?', '?', 3, 3, 2, 2, -3, -3, -4, -4, 12, 12, 0, 0, 8, 8, 0, 0, -1, -1, 12, 12]
19845 126*a-63 8 [2] [-3, '?', '?', '?', -4, -4, 4, 4, 2, 2, 0, 0, -2, -2, -12, -12, -2, -2, 0, 0, -16, -16, 14, 14]
19845 126*a-63 9 [2] [3, '?', '?', '?', 2, -4, -2, 4, -8, 4, 0, 6, -2, -2, -4, -4, -8, 4, -8, 10, 0, 0, -6, 18]
19845 126*a-63 10 [2] [-1, '?', '?', '?', 6, -2, -2, -2, 6, 6, -2, -2, -6, 10, 0, 0, 14, -2, -10, -2, 4, -12, 10, 10]
19845 126*a-63 11 [2] [-1, '?', '?', '?', -2, 6, -2, -2, 6, 6, -2, -2, 10, -6, 0, 0, -2, 14, -2, -10, -12, 4, 10, 10]
19845 126*a-63 12 [2] [-1, '?', '?', '?', 2, 0, -6, 4, 8, -4, -8, -6, 6, -2, -4, -4, -4, 0, -12, 10, -8, 8, -6, 2]
19845 126*a-63 13 [2] [-3, '?', '?', '?', 0, 0, -8, -8, -2, -2, 4, 4, -6, -6, 4, 4, -2, -2, -12, -12, 8, 8, -6, -6]
19845 126*a-63 14 [2] [-1, '?', '?', '?', -6, 2, -2, -2, -6, -6, -2, -2, 6, -10, 0, 0, 14, -2, 10, 2, 4, -12, -10, -10]
19845 126*a-63 15 [2] [-1, '?', '?', '?', 2, -6, -2, -2, -6, -6, -2, -2, -10, 6, 0, 0, -2, 14, 2, 10, -12, 4, -10, -10]
19845 126*a-63 16 [2] [-1, '?', '?', '?', 0, -2, 4, -6, 4, -8, -6, -8, 2, -6, 4, 4, 0, -4, -10, 12, 8, -8, -2, 6]
19845 126*a-63 17 [2] [-1, '?', '?', '?', -2, 0, -6, 4, -8, 4, -8, -6, -6, 2, 4, 4, -4, 0, 12, -10, -8, 8, 6, -2]
19845 126*a-63 18 [2] [-1, '?', '?', '?', 0, 2, 4, -6, -4, 8, -6, -8, -2, 6, -4, -4, 0, -4, 10, -12, 8, -8, 2, -6]
19845 126*a-63 19 [2, 3] [-1, '?', '?', '?', -6, 0, 8, 2, 6, -6, -10, 8, 6, -6, 12, 0, -4, 8, -12, -6, 8, -4, -6, -6]
19845 126*a-63 20 [2, 3] [-1, '?', '?', '?', 0, -6, 2, 8, -6, 6, 8, -10, -6, 6, 0, 12, 8, -4, -6, -12, -4, 8, -6, -6]
19845 126*a-63 21 [2] [-3, '?', '?', '?', 0, 0, -8, -8, 2, 2, 4, 4, 6, 6, -4, -4, -2, -2, 12, 12, 8, 8, 6, 6]
19845 126*a-63 22 [2] [3, '?', '?', '?', -4, 2, 4, -2, 4, -8, 6, 0, -2, -2, -4, -4, 4, -8, 10, -8, 0, 0, 18, -6]
19845 126*a-63 23 [2] [3, '?', '?', '?', 0, 0, 0, 0, -8, -8, -4, -4, 4, 4, -8, -8, 10, 10, -16, -16, 8, 8, 12, 12]
19845 126*a-63 24 [2] [3, '?', '?', '?', -6, -6, 6, 6, 2, 2, -10, -10, 2, 2, 8, 8, -2, -2, 10, 10, -4, -4, -6, -6]
19845 126*a-63 25 [2] [-3, '?', '?', '?', 4, 4, 4, 4, 2, 2, 0, 0, -10, -10, 4, 4, -2, -2, 8, 8, 0, 0, 6, 6]
19845 126*a-63 26 [5] [0, '?', '?', '?', 3, 3, 0, 0, -5, -5, 2, 2, -2, -2, 10, 10, -8, -8, 8, 8, 5, 5, 0, 0]
19845 126*a-63 27 [2] [1, '?', '?', '?', -4, 4, -8, 0, -6, 10, 4, -4, -6, -6, 4, -12, 6, -10, 0, 8, -8, 8, -6, -6]
19845 126*a-63 28 [2, 3] [-1, '?', '?', '?', 0, 6, 2, 8, 6, -6, 8, -10, 6, -6, 0, -12, 8, -4, 6, 12, -4, 8, 6, 6]
19845 126*a-63 29 [2, 3, 5] [-1, '?', '?', '?', 0, 0, -4, -4, 0, 0, 8, 8, 0, 0, 0, 0, 2, 2, 0, 0, -16, -16, 0, 0]
19845 126*a-63 30 [5] [0, '?', '?', '?', -3, -3, 0, 0, 5, 5, 2, 2, 2, 2, -10, -10, -8, -8, -8, -8, 5, 5, 0, 0]
19845 126*a-63 31 [2] [1, '?', '?', '?', -4, 4, 0, -8, -10, 6, -4, 4, 6, 6, 12, -4, -10, 6, -8, 0, 8, -8, 6, 6]
19845 126*a-63 32 [2] [1, '?', '?', '?', 4, -4, -8, 0, 6, -10, 4, -4, 6, 6, -4, 12, 6, -10, 0, -8, -8, 8, 6, 6]
19845 126*a-63 33 [3] [-4, '?', '?', '?', -3, -3, 2, 2, 3, 3, -4, -4, -12, -12, 0, 0, 8, 8, 0, 0, -1, -1, -12, -12]
19845 126*a-63 34 [2] [3, '?', '?', '?', 4, -2, 4, -2, -4, 8, 6, 0, 2, 2, 4, 4, 4, -8, -10, 8, 0, 0, -18, 6]
19871 -11*a-136 0 [] [-1, -1, -2, 8, -2, -5, 1, -3, 0, -3, '?', '?', -3, -6, -3, 0, 0, -2, -6, -1, -4, 6, -9, 1]
19871 -129*a+95 0 [] [-1, -1, -2, 8, -2, -5, 1, -3, 0, -3, '?', '?', -3, -6, -3, 0, 0, -2, -6, -1, -4, 6, -9, 1]
19871 -11*a-136 1 [] [2, 4, 2, -5, -3, -5, 1, -2, 6, 9, '?', '?', -6, -5, 14, -8, 15, -10, 6, -10, 13, 8, 5, -9]
19871 -129*a+95 1 [] [2, 4, -2, 3, 3, 3, 3, 2, 10, 3, '?', '?', 0, -9, 6, 10, -3, 0, 0, -6, -1, 8, -9, 3]
19871 -11*a-136 2 [2] [1, 4, -2, -6, 0, 2, -6, 4, 8, -2, '?', '?', -10, -10, -12, -4, -6, -8, 12, -8, -8, 2, -10, -14]
19871 -129*a+95 2 [2] [-3, 2, -2, 2, 4, -4, 4, -4, -2, -2, '?', '?', -6, -6, 12, -4, 6, -2, -8, 0, 0, 16, 10, -6]
19871 -11*a-136 3 [2] [-3, 2, -2, 2, -4, 4, -4, 4, -2, -2, '?', '?', -6, -6, -4, 12, -2, 6, 0, -8, 16, 0, -6, 10]
19871 -129*a+95 3 [] [2, 4, 2, -5, -3, -5, 1, -2, 6, 9, '?', '?', -6, -5, 14, -8, 15, -10, 6, -10, 13, 8, 5, -9]

Primes_Occuring = [] for l in Potential_primes1: for p in l: if p not in Primes_Occuring: Primes_Occuring.append(p)

Primes_Occuring

[2, 5, 7, 3, 67, 43, 37, 17, 13, 11, 19]

[2, 5, 7, 3, 67, 43, 37, 17, 13, 11, 19]

def possible_isogeny_degrees(aplist, isog_degree_bound): P = PrimeList w = set(primes(isog_degree_bound+1)) i = 0 R.<x> = ZZ[] while len(w) > 0 and i < len(P): if aplist[i] in ZZ: frob = x^2-aplist[i]*x+Norms[i] w = [ell for ell in w if not frob.change_ring(GF(ell)).is_irreducible()] i += 1 else: i += 1 return w

aplist1 = aplist_from_data(F.readline()) possible_isogeny_degrees(aplist1, 100)

[2]

[2]

def aplist_from_data(fline): fstrngs = fline.split() ap = [] for e in fstrngs[3:]: try: ap.append(int(e)) except: ap.append(e) return ap

aplist_from_data(F.readline())

in aplist
['?', 2, -2, 10, -4, -4, 4, 4, -2, -2, 0, 0, 2, 2, 12, 12, -10, -10, 8,
8, -16, -16, -6, -6]

in aplist
['?', 2, -2, 10, -4, -4, 4, 4, -2, -2, 0, 0, 2, 2, 12, 12, -10, -10, 8, 8, -16, -16, -6, -6]

Isogeny Degrees

335 days ago by adeines