curve #3944

y² + xy + y = x³ − x² − 114986178841097696x + 15007193935328647166383491

a-invariants: [1, -1, 1, -114986178841097696, 15007193935328647166383491]
c-invariants: [5519336584372689393, -12966215535286936522078234185]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1354000263461127126
discriminant (Δ): 7654144671633140700386977387894433429066165362944
Faltings height: 8.4560
naive height: 129.4644
primes of bad reduction: 2, 3, 13, 19, 31, 37, 59, 109, 163, 241, 1051
regulator: 128047967.5691548883955931150683056052836895166917247
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:31:31 UTC
last updated: 2026-10-05 04:31:31 UTC

Witness: 7 independent points log in to add more points →

(24930430451993/2809, -124389699933139204539/148877)
(108276380530713/38809, -1118730119383494649163/7645373)
(873793217, -24118623325851)
(3213661092329/15625, -470208470526303267/1953125)
(64296090680657/1681, -515538320422833376131/68921)
(209386365969/625, -58645785666770847/15625)
(96356131460753/485809, 19385016699743523777/338608873)

Commentary

Unlisted rational-isogeny neighbor of curve#3663 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:31:31 UTC · history