curve #5618

← home · all curves · JSON ↓

y² + y = x³ − 457757980040129578307379451998919

a-invariants: [0, 0, 1, 0, -457757980040129578307379451998919]
c-invariants: [0, 395502894754671955657575846527065800]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 148313585533001983371590942447649675
discriminant (Δ): -90522303101461297185157176682834994912024195217051617443942105051875
Faltings height: 11.7186
naive height: 163.9309
primes of bad reduction: 3, 5, 13, 19, 23, 31, 41, 59, 167, 199, 349
regulator: 3703167534576.70644736725315533837605987359222008933069
submitted by: Maksym Voznyy
submitted at: 2026-10-23 23:31:27 UTC
last updated: 2026-10-23 23:31:27 UTC

Witness: 8 independent points log in to add more points →

(74417349928067929/34596, 20300246573170756046527655/6434856)
(4706052657703921/54756, 170511776292086484537979/12812904)
(462227122965862883900630308430085848469790743072389931529/1066913597996100483279938382972115908850418064, -9909626584729508279460160397489530138061168051459357481186893326957110597143195846789/34849285268176558506013320139290778748773359823522307658626403016512)
(1649574121242636437046818551159893263900627467333745913918948346544721418071850199519650509889/17091078346303372022361609875024831572248466472344441958589687238104455710614278244, 46939767230333020776237939065006475059362365536619159280617298286369199003578760223768321030000297175693243723631750175152474751985419658677/2234365399903849691958338141074415308342816457678215698163515790863483378209161704672170677850917072820176157727209366762472)
(3295740601504773103628402792366761/4687860849283921288464, -189078995332684734348710253019673787386647240682315/320968245243750106867974412581312)
(81542293027695271334645330111774071160401/1050412063626799963100731183104, -3413263824498649801698135857980678010840615528890082936313895/1076563251915264979759789162072846340992008192)
(16455655129948196643927834250293139609/109830603222385206986318400, 62044646645663336340120983109649737665760190740801571523/1151025786657373244561315913387037248000)
(2109697180956200273901959061915851437663129/27368530631093680612391777117184, -76392666974373328089492242279276442577356107292033300685611709/143178306817184550748103126091805194398339530752)

Commentary

Voznyy (2023), A = -222346265640630885, [r, s, t] = [64, 279, 299] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-23 23:31:27 UTC · history