curve #3805

y² = x³ + x² − 2701980700587571800x + 1482064062724005771342622500

a-invariants: [0, 1, 0, -2701980700587571800, 1482064062724005771342622500]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 445323314722125840
discriminant (Δ): 313592381356490288834487338315428200485189506947600000000
Faltings height: 9.5661
naive height: 138.9352
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 61, 103, 151, 263
regulator: 18718.091130674647024106046243342563179682619313584
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 11:15:42 UTC
last updated: 2026-10-02 11:15:42 UTC

(-1573771350, 42854589414000)
(-680036430, 54818125053120)
(-72558702, 40960154670864)
(641359800, 3597323497350)
(648397248, 1644910223814)
(1403381400, 21309277304250)

(u,v) = (55575,23851) 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 11:15:42 UTC · history