Height difference bound

x=var('x') K.<a> = NumberField(x^2-x-1) 

E = EllipticCurve(K,[0,a+1,a,6*a-7,10*a-15]) def h_inf(x): return (1/K.degree())*((1)*log(max(1,x.abs()))+(1)*log(max(1,x.abs(i=1)))) 

def h(D): sum=0 for t in range(len(D.factor())): n_p=1 n=D.factor()[t][0].norm()%5 if n==0 or n==2 or n==3: n_p=2 x_v=(D.factor()[t][0].norm())^(D.factor()[t][1]/n_p) y=n_p*max(0,log(x_v)) sum+=y sum+= max(0,log(D.abs())) + max(0,log(D.abs(i=1))) sum=.5*sum return float(sum) 

def mu(E): if E.b2()==0: q = 0 else: q = 1 return (1/12)*h(E.discriminant()) + (1/12)*h_inf(E.j_invariant()) + (1/2)*h_inf(E.b2()/12) + (1/2)*log(q) 

upper_bound = (1/12)*h(E.j_invariant()) + 2*mu(E) + 1.922 print upper_bound 

7.26094117886051

7.26094117886051