curve #3581

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y² + xy + y = x³ − 1065725121464552797358276993065048x + 12296003729998120618135688362808500359797284582178

a-invariants: [1, 0, 1, -1065725121464552797358276993065048, 12296003729998120618135688362808500359797284582178]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 33592578908585391301525577089918025264264493082392027052304585818711675097733496192170
discriminant (Δ): 12151976373148286032139226150705550480221543555260589903797958513546616671138683800947555816332812500 ★ record for rank ≥ 24
Faltings height: 17.9438 ★ record for rank ≥ 24
naive height: 239.7605 ★ record for rank ≥ 24
primes of bad reduction: 2, 3, 5, 11, 17, 37, 4133, 13181887, 437158892239, 3346498881309878821, 119441939999490408530514287704804310357
regulator: 51506412651316838220410620926.789365030910114030662618703975536306452483026097655304213
submitted by: Matej Jurasić
submitted at: 2026-09-28 21:00:50 UTC
last updated: 2026-09-28 21:00:50 UTC

Witness: 24 independent points log in to add more points →

(34082455445867659, -3945139342194706875360205)
(25689322064533909, 1368097802823724391472545)
(377050505879853511/4, -219001826934759870416138015/8)
(119221423675786951/4, -21180444758088068736509375/8)
(2596728120896540659, 4184133679031626607623791545)
(151852011270419659, 57896667265219729808460545)
(23986152648626884, -730372427397061505081530)
(208677104839403056/9, 6089403742326968112952715/27)
(12823190472320509, 859406039175392725307645)
(11677566916377994, -1201393100428620289068670)
(12319682577081034, 1018048692685303371743795)
(987192651696357784, 980320436317738158422398670)
(92790583793509111/4, 1910927395780806541254685/8)
(23335928471383402, 366416999372453760815042)
(33458588551878034, 3754260318648571718781170)
(-5678151411591015566/361, -34409628816419473702240747975/6859)
(25598057013699484, -1337500492514333719077130)
(-8733720526801007654059899341/268765517476, -494845586279706211876142741217717815888405/139335032163012776)
(-18908696409475219507841859329/801406315369, -3537024983226722322169046170209068531751385/717429351800428597)
(41912139576597510511772179/1721503081, -63106169584237951126878187563612020005/71426884333771)
(-8390449759577704732536497318291/295473787801201, -22520609901889213168421965527296630741405329205/5079002649814362210551)
(4342835332672818103590592160334/181768341658201, 1683648365272655044785762317225754021386662955/2450627865718772953949)
(14504440455051923026577075584/420745525201, 1109431119131453671795986268092318574163705/272916164176103449)
(-4169965334272607951031582701/2992533251236, 19215731524837869520087739502912278089571705/5176765316113648984)

Commentary

Specialization at T = 241/69 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).

last edited by Matej Jurasić at 2026-09-28 21:00:51 UTC · history