def change_iso_curve(self, a):
"""
INPUT:
* a the montgomery a coefficient of the target curve
OUTPUT:
* the point P seen in the new curve
"""
a1 = self.curve.Fp2(self.curve.a)
if (a**2 - 4) * (a1**2 - 3)**3 != (a1**2 - 4) * (a**2 - 3)**3:
# i.e if 256*(a1**2 - 3)**3/(a1**2 - 4) != 256*(a**2 - 3)**3/(a**2 - 4)
raise RuntimeError('the curves are not isomorphic.')
E_a1 = EllipticCurve(self.curve.Fp2, [0, a1, 0, 1, 0])
E_a = EllipticCurve(self.curve.Fp2, [0, a, 0, 1, 0])
xP = self.x / self.z
yP = sqrt(xP**3 + a1 * xP**2 + xP)
P_ws = E_a1(xP, yP)
iso = E_a1.isomorphism_to(E_a)
curve_target = copy(self.curve)
curve_target.a = a
return Point(iso(P_ws)[0], 1, curve_target)
