1024

295 days ago by Ben.LeVeque

ch = var('ch') K.<a>=NumberField(ch^2-ch-1);K 
        
Number Field in a with defining polynomial ch^2 - ch - 1
Number Field in a with defining polynomial ch^2 - ch - 1
def ap(E,p): return E.change_ring(K.residue_field(p)).trace_of_frobenius() def ap_list(E): aplist=[] for p in [2,3,5,7,11,19,29,31,41,59,61,71,79,89]: for i in K.primes_above(p): try: aplist.append(ap(E,i)) except: aplist.append('?') return aplist 
       
### 1024 32 ['?',-2,-2,6,0,-4,-4,-8,6,-2,8,-8,6,-10,8,-12,-2,14,0,8,-8,-8,10,-6] ###aps to check against 
       
f = open('/Users/bleveque/Sage/1024.txt') ### .txt version of saved file for line in f.readlines(): try: a4 = eval(line.split('x ')[0].split('^3')[1]) except SyntaxError: a4 = eval(line.split('x ')[0].split('^3')[1]+'1') try: a6 = eval(l.split('x ')[0].split('^3')[1]) except SyntaxError: a6 = eval(l.split('x ')[0].split('^3')[1]+'1') E = EllipticCurve(K,[a4,a6]) try: if set([ap(E,K.primes_above(89)[0]), ap(E,K.primes_above(89)[1])]) == set([-6,10]): print ap_list(E) except ArithmeticError: print 'Arith Error encountered' 
        
['?', '?', '?', -10, '?', 3, '?', 7, -9, 10, 0, -8, -7, 11, 4, -6, 11,
-14, 8, 7, -8, 9, 10, -6]
['?', '?', '?', -10, '?', 3, '?', 7, -9, 10, 0, -8, -7, 11, 4, -6, 11,
-14, 8, 7, -8, 9, 10, -6]
Arith Error encountered
Arith Error encountered
Arith Error encountered
Arith Error encountered
Arith Error encountered
Arith Error encountered
['?', '?', '?', -10, '?', 3, '?', 7, -9, 10, 0, -8, -7, 11, 4, -6, 11, -14, 8, 7, -8, 9, 10, -6]
['?', '?', '?', -10, '?', 3, '?', 7, -9, 10, 0, -8, -7, 11, 4, -6, 11, -14, 8, 7, -8, 9, 10, -6]
Arith Error encountered
Arith Error encountered
Arith Error encountered
Arith Error encountered
Arith Error encountered
Arith Error encountered
### The ap-values only match at 89 for two curves, but both of these have different ap-values at other primes than the curve we are looking for... Could be a parsing problem, but I *think* I figured out how to parse it correctly. ### 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
 
       
for i in range(30): li=f.readline() 
       
l=f.readline() 
       
try: print eval(l.split('x ')[0].split('^3')[1]) except SyntaxError: print eval(l.split('x ')[0].split('^3')[1]+'1') 
        
-44
-44
for i in range(30): l=f.readline() try: print eval(l.split('x ')[1].split('o')[0]) except SyntaxError: print 0 
        
112
-224*a - 112
14
-28*a - 14
5914432*a + 3655320
-25053936*a - 15484184
47315456*a + 29242560
-200431488*a - 123873472
-5914432*a - 3655320
25053936*a + 15484184
-47315456*a - 29242560
200431488*a + 123873472
670680*a - 1085184
158328*a - 256176
5365440*a - 8681472
1266624*a - 2049408
-670680*a + 1085184
-158328*a + 256176
-5365440*a + 8681472
-1266624*a + 2049408
-670680*a - 414504
2841048*a + 1755864
-5365440*a - 3316032
22728384*a + 14046912
670680*a + 414504
-2841048*a - 1755864
5365440*a + 3316032
-22728384*a - 14046912
-1512
3024*a + 1512
112
-224*a - 112
14
-28*a - 14
5914432*a + 3655320
-25053936*a - 15484184
47315456*a + 29242560
-200431488*a - 123873472
-5914432*a - 3655320
25053936*a + 15484184
-47315456*a - 29242560
200431488*a + 123873472
670680*a - 1085184
158328*a - 256176
5365440*a - 8681472
1266624*a - 2049408
-670680*a + 1085184
-158328*a + 256176
-5365440*a + 8681472
-1266624*a + 2049408
-670680*a - 414504
2841048*a + 1755864
-5365440*a - 3316032
22728384*a + 14046912
670680*a + 414504
-2841048*a - 1755864
5365440*a + 3316032
-22728384*a - 14046912
-1512
3024*a + 1512
set([2,3])== set([3,2]) 
        
True
True
eval('+ 1') 
        
1
1