curve=(0, 0, 0, 0, -1516563)
P=(Fraction(6403, 9), Fraction(511280, 27)); on_curve=True
q=6399; P_prime=(6399, 511920); phi_3(P_prime)=(Fraction(6403, 1), Fraction(511280, 1))
symbolic 3-isogeny identity and rational order-3 kernel check passed
discriminant=-993584159842608=-(2^4)(3^13)(79^4)
z(P)=-19209/511280; v_3(z(P))=1
2P=(Fraction(1737501484979929, 9410660582400), Fraction(63098649487407069202717, 28868895255416832000))
z(2P)=-5330098555443228594720/63098649487407069202717; v_2(z(2P))=5
special_points_F2=[(0, 1), (1, 0)]; smooth_locus_F2=['O', (1, 0)]
p=3 Hensel datum: -1516562 == 1 mod 3, root 1 simple
P mod 79=(18, 67); nonsingular=True
p=79 Hensel datum: -243 == 73 == 28^2 mod 79, root 28 simple
#E(F_5)=6; points=[(2, 0), (3, 2), (3, 3), (4, 1), (4, 4)]
#E(F_13)=21; points=[(0, 2), (0, 11), (2, 5), (2, 8), (4, 4), (4, 9), (5, 5), (5, 8), (6, 5), (6, 8), (7, 3), (7, 10), (8, 3), (8, 10), (10, 4), (10, 9), (11, 3), (11, 10), (12, 4), (12, 9)]
all exact assertions passed
