def granvsym2():
    K.<x>=QQ[]
    #on 617*x1^2+4*x1^4+4-y1^2=0
    n=8 #change to arbitrary large even
    E=EllipticCurve(QQ,[0, 0, 0, -380881/3, 469059442/27])
    P=E.gens()[0]
    h=(-x^2-5*x+1)^(2*n)
    f=(-x^2+5*x+1)^(2*n) + h
    g=(617*x^2+4*x^4+4)
    for k in [ 2 .. 10]:
        u,v=(k*P).xy()
        u= -u
        x1,y1=-36/(380113+3702*u+9*u^2)*v, -1/2*(-7611476-29616*u+36*u^2)/(380113+3702*u+9*u^2)
        x2=1/2/(-1+x1^2)*(-25*x1+(y1 ))
        print k,QQ(f(x1)/f(x2)).is_square(),g(x1)-y1^2==0,'---','x2squ=',QQ(g(x2)).is_square()