curve #3991

y² + xy + y = x³ + x² − 3546566101391022206530x − 45048773556845244140445824700049

a-invariants: [1, 1, 1, -3546566101391022206530, -45048773556845244140445824700049]
c-invariants: [170235172866769065913441, 38922140351837527140844424546491375]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
conductor (N): 5823102912675542002999614449352786
discriminant (Δ): 1978289755317522871792254824288020695298141269616499352705717246432
Faltings height: 11.4191
naive height: 160.4744
primes of bad reduction: 2, 3, 11, 19, 23, 47, 97, 107, 109, 271, 353, 563, 1153, 1291, 5051, 9377
regulator: 863164056985025.77788779825544421733488232095770178005790680580
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:40:56 UTC
last updated: 2026-10-05 04:40:56 UTC

Witness: 12 independent points log in to add more points →

(-891007252471698059/17363889, 97729782068624315246859133/72355325463)
(-778716859771/16, 224232888334709949/64)
(-22883730282011/1521, -131366499086420430019/59319)
(-20654609951281/1369, -113548950865083680499/50653)
(-49776203444859/2401, -520407056893803560321/117649)
(570200153981, -428160135259331589)
(374684088231, -226334721398978393)
(22696445236869/169, 95786829866731989907/2197)
(62014931434979/169, 481664502292446855537/2197)
(-2622960703528009/180625, 141356030846575417675311/76765625)
(-45757347016489/1849, -417413199965872499067/79507)
(-5619942358727819/269361, -623074365630163750244807/139798359)

Commentary

Unlisted rational-isogeny neighbor of curve#3633 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 12: 12 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 04:40:56 UTC · history