curve #4288

y² + xy = x³ + x² + 425915423867x + 69866881484043667

a-invariants: [1, 1, 0, 425915423867, 69866881484043667]
c-invariants: [-20443940345591, -60364832272661136293]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 884834993897161758496110
discriminant (Δ): -7053561264439215292420703292146631390
Faltings height: 5.7583
naive height: 91.9461
primes of bad reduction: 2, 3, 5, 13, 23, 29, 53, 83, 97, 311, 599, 1871, 22871
regulator: 2348706693.220088930790402196579874536581790948742995177245
submitted by: The Wren
submitted at: 2026-10-16 18:46:26 UTC
last updated: 2026-10-16 18:46:26 UTC

Witness: 10 independent points log in to add more points →

(3549, -267169325)
(1073519, 1327720040)
(4568271/4, 11438265383/8)
(643089, 780528656)
(97253, 334926416)
(-88947, 176903971)
(430737, -577485808)
(875987, -1056447304)
(692303/4, -3086319077/8)
(-128209/4, 1896354463/8)

Commentary

Obtained by a rational 2-isogeny from curve#4056, submitted by NDElkies. This isogenous curve has the same rank and conductor. The ten supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 18:46:26 UTC · history