SHA.3

476 days ago by pub

v = open(DATA + 'SHA.3').readlines() 
       
len(v) 
        
630
e = [EllipticCurve(eval(w.split()[0])) for w in v] 
       
ee = [(x.conductor(), x) for x in e] 
       
ee.sort() 
       
E = ee[0][1] 
       
E 
        
Elliptic Curve defined by y^2 + x*y  = x^3 - x^2 + 94*x + 9 over
Rational Field
E.conductor() 
        
53295337
h = lambda x: QuadraticField(x,'a').class_number() 
       
[(h(D), D) for D in E.heegner_discriminants_list(10)] 
        
[(1, -7), (1, -8), (3, -23), (2, -24), (4, -39), (5, -47), (2, -52),
(4, -55), (4, -56), (3, -83)]
time E.rank() 
        
2
CPU time: 0.03 s,  Wall time: 0.56 s
time E.gens() 
        
[(0 : 3 : 1), (8 : 31 : 1)]
CPU time: 0.41 s,  Wall time: 2.19 s
L = E.lseries() 
       
ld = L.dokchitser(10) 
       
ld(1) 
        
-9.8e-10
ld.derivative(1,2) 
        
130.
F = E.quadratic_twist(-7) 
       
F.rank(proof=False) 
        
1
factor(F.conductor()) 
        
7^2 * 53295337
2+3 
       
time F.sha().an_numerical(prec=15,proof=False) 
        
1.000
CPU time: 0.46 s,  Wall time: 2391.85 s
s = E.sha() 
       
time san = s.an_numerical(prec=15, proof=False); san 
        
9.003
CPU time: 0.12 s,  Wall time: 35.44 s