curve #3984

y² = x³ − x² − 720802923633795608x + 266350778655524200306865712

a-invariants: [0, -1, 0, -720802923633795608, 266350778655524200306865712]
c-invariants: [34598540334422189200, -230127072550781667058598840000]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 43316108595835552276361984400
discriminant (Δ): -6679384062133394302819553246171750519350663802304000000
Faltings height: 9.2477
naive height: 135.2169
primes of bad reduction: 2, 3, 5, 11, 43, 191, 199, 227, 263, 269, 421, 449, 1571
regulator: 16420647530494.2089678650209534560278862150191163009794713347
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:39:32 UTC
last updated: 2026-10-05 04:39:32 UTC

Witness: 11 independent points log in to add more points →

(4133892628/9, 153155533731200/27)
(910564717, 19104655581550)
(-61579850511/64, 4256237025305001/512)
(1035000996, 25080672031008)
(168503654485252/80089, 2035232516846019147488/22665187)
(69493804708, 18318372842125664)
(10077117498373/45369, 104620621637406846950/9663597)
(20200944741/25, 1817892438597114/125)
(440842737093828/3575881, 90560773856920067445024/6761990971)
(2034754261588/4761, 1980792618826890176/328509)
(-15078160279576412/16265089, 770281040914559571332000/65597103937)

Commentary

Unlisted rational-isogeny neighbor of curve#3622 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 11: 11 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 04:39:32 UTC · history