curve #5543

y² = x³ − x² − 9149453339881480725104x + 277647966337996584927833599179264

a-invariants: [0, -1, 0, -9149453339881480725104, 277647966337996584927833599179264]
c-invariants: [439173760314311074805008, -239887842913394006815762363242054080]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 11916990873131684484144
discriminant (Δ): 15716923249956014444108874161424395167554281791460109030164644859904
Faltings height: 11.6120
naive height: 163.3175
primes of bad reduction: 2, 3, 7, 11, 13, 19, 29, 41, 43, 71, 97, 181, 239, 857
regulator: 329462.5619993971892941719394493427417294605281950661
submitted by: Daniel Błażewicz
submitted at: 2026-10-23 00:09:49 UTC
last updated: 2026-10-23 00:09:49 UTC

(-26346336600, 22369952515441608)
(20166365185, 10066680312370132)
(30577867594, 5144675189982394)
(73512792770, 1522773559105722)
(100057245320, 19076090056695672)
(-1576914257019/49, 7961479406162135358/343)
(8860022543289352/96721, 434027729305799395541320/30080231)

(u,v) = (195263,425929) 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 00:09:49 UTC · history