curve #5550

y² = x³ + x² − 89073270797603515461524x + 10230672098515574129127973163724096

a-invariants: [0, 1, 0, -89073270797603515461524, 10230672098515574129127973163724096]
c-invariants: [4275516998284968742153168, -8839300693143109149556278625910537920]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 3225632506223974541448
discriminant (Δ): 13546851644568695869150611429288493133873528281266975657073851250944
Faltings height: 11.8872
naive height: 170.1448
primes of bad reduction: 2, 3, 13, 17, 29, 37, 61, 107, 251, 523, 653, 1013
regulator: 3269121.730040409372141789643825226753514111825348165
submitted by: Daniel Błażewicz
submitted at: 2026-10-23 01:31:52 UTC
last updated: 2026-10-23 01:31:52 UTC

(4033142590414, 8078059630277331750)
(2712855426526/25, 5365903855660634574/125)
(8701925927986/49, 1237755572110737030/343)
(14078105873035/49, 31352803105669845192/343)
(36961928115889/400, 422479160137398403887/8000)
(1009127094040528/1849, 28017861125221547798400/79507)
(425081513333177335/1907161, 100295830957289604476051394/2633789341)

(u,v) = (58682,720171) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 7.

last edited by Daniel Błażewicz at 2026-10-23 01:31:52 UTC · history