curve #381

y² + xy = x³ − x² − 109823651656505846940102737179x + 13881034132195426802661701381391692661966985

a-invariants: [1, -1, 0, -109823651656505846940102737179, 13881034132195426802661701381391692661966985]
c-invariants: [5271535279512280653124931384601, -11993213490216825035590952188259483397748244349]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 529977280406126175169004910669809692117809596897853827769555535980969490
discriminant (Δ): 1535861076553756069541566097526976300456021823719770432861083465864224153832843577587500
Faltings height: 15.5461
naive height: 212.2196
primes of bad reduction: 2, 5, 7, 13, 17, 19, 137, 2927, 9857, 22877, 751717, 26526005013529182718611541831083756937467758339
regulator: 1233663567030839841866.846731820081714564884700348414590649388725882158702816
submitted by: y011d4
submitted at: 2026-08-27 02:22:38 UTC
last updated: 2026-08-27 02:22:38 UTC

(33350919790840623953689/365459689, 15014934430749107259292983880423241/6986492874613)
(30213406011258635211984/41306329, 4785095466654355878893205236864441/265475776483)
(308921569196098245509/1752976, 14789176861081784368484288523/2320940224)
(552675041032428311809/3150625, 658535318199635745125055464827/5592359375)
(-270477440380364, 4878345486534318159767)
(-194796714244350379/529, -25493145234444233576460426/12167)
(264464575450879, -1825820745592771366113)
(-190311383075685, 5280998778095289127810)
(-160004356688939, 5230388427142704316442)
(6902190585171, -3622614967766709035198)
(-204830294291751884/625, 59852897580026515536119261/15625)
(220991273122859, 635254087362035177427)
(159326168021461, -654003059405995000303)
(209614049980916, 265492499496359062837)
(1880284674205504/9, -6362922112354755567151/27)
(40515457220232691/196, 299730923017663390177063/2744)
(-204153064988810, -5271914258603485390065)
(18277656280720739/4, -2464718585508415172578999/8)
(117616379001518964/529, 8199242391185828924084129/12167)

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last edited by y011d4 at 2026-08-27 02:26:00 UTC · history