curve #3802

y² = x³ − x² − 6064909050029386964x + 4169102678346307373750224644

a-invariants: [0, -1, 0, -6064909050029386964, 4169102678346307373750224644]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 4857168842595394248
discriminant (Δ): 6768750246670703211235241542073735193029448774908991777024
Faltings height: 9.8043
naive height: 141.3608
primes of bad reduction: 2, 3, 7, 11, 19, 31, 37, 41, 43, 59, 103, 11257
regulator: 144489.63085585140034225241045445463008852332880889
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 08:48:33 UTC
last updated: 2026-10-02 08:48:33 UTC

(92093009, 60094492315704)
(5216368550, 338337557307288)
(-99681233636/121, 123477448565625574/1331)
(17177099524/25, 2258188054009118/125)
(2900479922764/11449, 63049659147518173130/1225043)
(107981233751457913485020/246247306368361, 154273005036578274470205636580873578/3864178972057733901109)

(u,v) = (68894,35123) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 6.

last edited by Daniel Błażewicz at 2026-10-02 08:48:33 UTC · history